Polygamy rhymes with:
burgamy, kagami, monogamy, academy, alchemy, anatomy, anomie, appendectomy, archenemy, astronomy, autonomy, barthelemy, bellamy, bellomy, blasphemy, burgamy, cheramie, dichotomy, economy, enemy, epitome, gastronomy, hysterectomies, hysterectomy, ideonomy, infamy, jeremy, kagami, keratotomy, laramee, laramie, lockamy, lumpectomy, mastectomy, mcmenamy, mcmenemy, mcnamee, metonomy, monogamy, nashnamie, pallidotomy, prostatectomy, ptolemy, sesame, sodomy, tonsillectomy, vasectomy
Polygamy sounds like:
palazina, paleocene, paulsen, paulson, pelagian, pelekunu, pelican, pelikan, pellicane, pellicano, peloquin, philson, phlegm, phylogeny, pilson, plasma, pliocene, polcyn, policeman, policemen, policewoman, policewomen, poliquin, polskin, polson, polygon, polygyny, polzin, populism, poulsen, poulson, powelson, pulcini