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 her".
Words that have a pure rhyme on their last syllable only.
stationer
    probationer
      vacationer
        bracer
          chaser
            facer
              lacer
                pacer
                  placer
                    racer
                      spacer
                        tracer
                          eraser
                            Acer
                              fresher
                                pressure
                                  thresher
                                    refresher
                                      Beshore
                                        Cheshire
                                          Drescher
                                            Escher
                                              Flesher

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                                                Words that "almost" rhyme on the vowel-based rhyme sound of the stressed syllable like: be/eat or maybe/shapely.
                                                stationer
                                                  probationer
                                                    vacationer
                                                      bracer
                                                        chaser
                                                          facer
                                                            lacer
                                                              pacer
                                                                placer
                                                                  racer
                                                                    spacer
                                                                      tracer
                                                                        eraser
                                                                          Acer
                                                                            ager
                                                                              gauger
                                                                                major
                                                                                  pager
                                                                                    stager
                                                                                      wager
                                                                                        Yager

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                                                                                          Rhymes made up of more than one word. For instance, "jealous" and "tell us" or "shaky" and "make me."