WikiRhymer has about 600 rhyming words and phrases for "unit" starting with...

Words that have identical vowel-based rhyme sounds in the tonic syllable. Moreover, that tonic syllable must start with a different consonantal sound.
Junot
    Pure Rhyme Set #1 of 1 (Add to/Edit Set Members)
    Words that have a pure rhyme on their last syllable only.
    donut
      doughnut
        Donat
          SONET
            End Rhyme Set #1 of 82 (Add to/Edit Set Members)
            diet
              quiet
                riot
                  disquiet
                    Guyot
                      Hiatt
                        Hyatt
                          Pyatt
                            Wiatt
                              Wyatt
                                • run riot
                                End Rhyme Set #2 of 82 (Add to/Edit Set Members)
                                granite
                                  planet
                                    Granat
                                      Janet
                                        End Rhyme Set #3 of 82 (Add to/Edit Set Members)

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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)
                                        boomlet
                                          intuit
                                            bluebonnet
                                              tunicate
                                                duplicate
                                                  Newmarket
                                                    Near Rhyme Set #1 of 1 * (Add to/Edit Set Members)
                                                    Rhymes made up of more than one word. For instance, "jealous" and "tell us" or "shaky" and "make me."

                                                    We have no mosaic rhymes for "unit".

                                                    Mosaic Rhyme Set #1 of 1 (Add to/Edit Set Members)