WikiRhymer has about 6,000 rhyming words and phrases for "touchin'" starting with...

clutchin'
    retouchin'
      Pure Rhyme Set #1 of 1 (Add to/Edit Set Members)
      Words that have a pure rhyme on their last syllable only.
      bunchin'
        crunchin'
          lunchin'
            munchin'
              punchin'
                truncheon
                  End Rhyme Set #1 of 657 (Add to/Edit Set Members)
                  blushin'
                    brushin'
                      crushin'
                        flushin'
                          gushin'
                            rushin'
                              End Rhyme Set #2 of 657 (Add to/Edit Set Members)
                              etchin'
                                fetchin'
                                  sketchin'
                                    stretchin'
                                      Chechen
                                        End Rhyme Set #3 of 657 (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)
                                        bunchin'
                                          crunchin'
                                            lunchin'
                                              munchin'
                                                punchin'
                                                  truncheon
                                                    Near Rhyme Set #1 of 64 (Add to/Edit Set Members)
                                                    blushin'
                                                      brushin'
                                                        crushin'
                                                          flushin'
                                                            gushin'
                                                              rushin'
                                                                Near Rhyme Set #2 of 64 (Add to/Edit Set Members)
                                                                budgin'
                                                                  fudgin'
                                                                    grudgin'
                                                                      judgin'
                                                                        nudgin'
                                                                          trudgin'
                                                                            curmudgeon
                                                                              Near Rhyme Set #3 of 64 (Add to/Edit Set Members)

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                                                                              Rhymes made up of more than one word. For instance, "jealous" and "tell us" or "shaky" and "make me."
                                                                              • ca + in
                                                                              • dah + in
                                                                              • huh + in
                                                                              • Sta + in
                                                                              • the + been
                                                                              • the + bin
                                                                              • the + Blinn
                                                                              • the + brin
                                                                              • the + Bryn
                                                                              • the + chin
                                                                              • the + din
                                                                              • the + fin
                                                                              • the + finn
                                                                              • the + Flinn
                                                                              • the + Flynn
                                                                              • the + gin
                                                                              • the + Ginn
                                                                              • the + Glyn
                                                                              • the + Glynn
                                                                              • the + grin
                                                                              • the + Gwin
                                                                              • the + Gwinn
                                                                              • the + Gwynne
                                                                              • the + gyn
                                                                              • the + in
                                                                              • the + inn
                                                                              • the + jin
                                                                              • the + kin
                                                                              • the + Knin
                                                                              • the + Lin
                                                                              • the + Linn
                                                                              • the + Linne
                                                                              • the + Lyn
                                                                              • the + Lynn
                                                                              • the + Lynne
                                                                              • the + min
                                                                              • the + pin
                                                                              • the + quin
                                                                              • the + Quinn
                                                                              • the + Schwinn
                                                                              • the + shin
                                                                              • the + sin
                                                                              • the + skin
                                                                              • the + spin
                                                                              • the + syn
                                                                              • the + thin
                                                                              • the + tin
                                                                              • the + twin
                                                                              • the + vin
                                                                              • the + when
                                                                              • the + win
                                                                              • the + Winn
                                                                              • the + Wynn
                                                                              • the + Wynne
                                                                              • the + yin
                                                                              • the + Zinn
                                                                              • uh + in
                                                                              Mosaic Rhyme Set #1 of 1 (Add to/Edit Set Members)