WikiRhymer has about 1,000 rhyming words and phrases for "furniture" 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.
Words that have a pure rhyme on their last syllable only.
Deringer
    Heringer
      nurture
        searcher
          Bircher
            Elenore
              Elinor

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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)
                nurture
                  searcher
                    Bircher
                      further
                        Werther
                          Birkner
                            Kirchner

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                              Rhymes made up of more than one word. For instance, "jealous" and "tell us" or "shaky" and "make me."
                              • her + pitcher
                              • her + richer
                              • were + richer
                              Words that rhyme on the vowel-based rhyme sound of the last syllable only (for instance: “maybe” and “eat”). Near End Rhymes generally (but not always!) suck. Nonetheless, we provide them for you just in case you may find something useful.
                              eastern
                                northeastern
                                  southeastern
                                    Mideastern
                                      govern
                                        McGovern
                                          freeborn
                                            Freeburn

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