Words that have identical vowel-based rhyme sounds in the tonic syllable. Moreover, that tonic syllable must start with a different consonantal sound.
There are none pure rhymes for "race me".
Words that have a pure rhyme on their last syllable only.
facie
    lacy
      racy
        Acey
          Bracey
            Casey
              Dacey
                Dacy
                  Daisey
                    Gracey
                      Gracie
                        Gracy
                          Lacey
                            Macey
                              Macy
                                Pacey
                                  Spacey
                                    Stacey
                                      Stacy
                                        Tacy
                                          Tracey
                                            Tracie
                                              Tracy
                                                Treacy
                                                  Kacy
                                                    jami
                                                      cockamamie
                                                        Amy
                                                          Jaimie
                                                            Jamie
                                                              Jayme
                                                                Mamie
                                                                  Noémi
                                                                    gamely
                                                                      lamely
                                                                        namely

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                                                                          Words that "almost" rhyme on the vowel-based rhyme sound of the stressed syllable like: be/eat or maybe/shapely. (Click for more info)
                                                                          facie
                                                                            lacy
                                                                              racy
                                                                                Acey
                                                                                  Bracey
                                                                                    Casey
                                                                                      Dacey
                                                                                        Dacy
                                                                                          Daisey
                                                                                            Gracey
                                                                                              Gracie
                                                                                                Gracy
                                                                                                  Lacey
                                                                                                    Macey
                                                                                                      Macy
                                                                                                        Pacey
                                                                                                          Spacey
                                                                                                            Stacey
                                                                                                              Stacy
                                                                                                                Tacy
                                                                                                                  Tracey
                                                                                                                    Tracie
                                                                                                                      Tracy
                                                                                                                        Treacy
                                                                                                                          Kacy
                                                                                                                            jami
                                                                                                                              cockamamie
                                                                                                                                Amy
                                                                                                                                  Jaimie
                                                                                                                                    Jamie
                                                                                                                                      Jayme
                                                                                                                                        Mamie
                                                                                                                                          Noémi
                                                                                                                                            gamely
                                                                                                                                              lamely
                                                                                                                                                namely

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                                                                                                                                                  Rhymes made up of more than one word. For instance, "jealous" and "tell us" or "shaky" and "make me."
                                                                                                                                                  Words that rhyme on the vowel-based rhyme sound of the last syllable only (for instance: “maybe” and “eat”). Near End Rhymes generally (but not always!) suck. Nonetheless, we provide them for you just in case you may find something useful.
                                                                                                                                                  crosspiece
                                                                                                                                                    decrease
                                                                                                                                                      earpiece
                                                                                                                                                        earpiece
                                                                                                                                                          eyepiece
                                                                                                                                                            increase
                                                                                                                                                              mouthpiece
                                                                                                                                                                showpiece
                                                                                                                                                                  sublease
                                                                                                                                                                    timepiece
                                                                                                                                                                      homies
                                                                                                                                                                        altarpiece
                                                                                                                                                                          centerpiece
                                                                                                                                                                            coyotes
                                                                                                                                                                              legalese
                                                                                                                                                                                masterpiece
                                                                                                                                                                                  verdigris
                                                                                                                                                                                    oncogenes
                                                                                                                                                                                      Greenpeace
                                                                                                                                                                                        Heidi's
                                                                                                                                                                                          Loise
                                                                                                                                                                                            Matisse
                                                                                                                                                                                              Sangiovese
                                                                                                                                                                                                Therese
                                                                                                                                                                                                  bireme
                                                                                                                                                                                                    bloodstream
                                                                                                                                                                                                      daydream
                                                                                                                                                                                                        jetstream
                                                                                                                                                                                                          mainstream
                                                                                                                                                                                                            midstream
                                                                                                                                                                                                              moonbeam
                                                                                                                                                                                                                nauseam
                                                                                                                                                                                                                  sidestream
                                                                                                                                                                                                                    sunbeam
                                                                                                                                                                                                                      academe
                                                                                                                                                                                                                        episteme
                                                                                                                                                                                                                          Purim
                                                                                                                                                                                                                            Saleem
                                                                                                                                                                                                                              beam
                                                                                                                                                                                                                                bream
                                                                                                                                                                                                                                  cream
                                                                                                                                                                                                                                    creme
                                                                                                                                                                                                                                      deem
                                                                                                                                                                                                                                        diem
                                                                                                                                                                                                                                          dream
                                                                                                                                                                                                                                            gleam
                                                                                                                                                                                                                                              ream
                                                                                                                                                                                                                                                scheme
                                                                                                                                                                                                                                                  scream
                                                                                                                                                                                                                                                    seam
                                                                                                                                                                                                                                                      seem
                                                                                                                                                                                                                                                        steam
                                                                                                                                                                                                                                                          stream
                                                                                                                                                                                                                                                            team
                                                                                                                                                                                                                                                              teem
                                                                                                                                                                                                                                                                theme
                                                                                                                                                                                                                                                                  agleam
                                                                                                                                                                                                                                                                    downstream
                                                                                                                                                                                                                                                                      esteem
                                                                                                                                                                                                                                                                        extreme
                                                                                                                                                                                                                                                                          passim
                                                                                                                                                                                                                                                                            redeem
                                                                                                                                                                                                                                                                              regime
                                                                                                                                                                                                                                                                                supreme
                                                                                                                                                                                                                                                                                  upstream
                                                                                                                                                                                                                                                                                    blaspheme
                                                                                                                                                                                                                                                                                      Hakim
                                                                                                                                                                                                                                                                                        Ibrahim
                                                                                                                                                                                                                                                                                          Joachim
                                                                                                                                                                                                                                                                                            Kareem
                                                                                                                                                                                                                                                                                              Karim
                                                                                                                                                                                                                                                                                                Maxime
                                                                                                                                                                                                                                                                                                  Reim
                                                                                                                                                                                                                                                                                                    Sephardim
                                                                                                                                                                                                                                                                                                      Vadim

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