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 no 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.
                                                                          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."