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 "p m".
Words that have a pure rhyme on their last syllable only.
mayhem
    Aleichem
      'em
        bem
          em
            femme
              gem
                hem
                  rem
                    stem
                      them
                        phlegm
                          tem
                            am
                              condemn
                                wm
                                  Behm
                                    Cardizem
                                      Chem
                                        Clem
                                          FM
                                            Jem
                                              Khem
                                                Klemm
                                                  Klemme
                                                    Lem
                                                      M
                                                        PM
                                                          Prem
                                                            Rehm
                                                              STIM
                                                                send'em
                                                                  postmortem
                                                                    diadem
                                                                      hominem
                                                                        stratagem
                                                                          diltiazem
                                                                            Aleichem
                                                                              Eminem
                                                                                Bethlehem
                                                                                  Words that "almost" rhyme on the vowel-based rhyme sound of the stressed syllable like: be/eat or maybe/shapely.
                                                                                  diltiazem
                                                                                    Rhymes made up of more than one word. For instance, "jealous" and "tell us" or "shaky" and "make me."