Exim rhymes with:
maxxim, maxxim, nissim, wasem, acronym, ahlgrim, anglim, antrim, beachem, chaim, dahlem, dershem, eidem, fillingim, ganem, ganim, gillem, goyim, hapoalim, hashem, hashim, hasidim, hatem, homonym, jachim, joachim, jochem, jochim, ketchem, knierim, laflamme, lathem, leathem, lockrem, maxxim, mechem, mellem, meriam, mitchem, naim, nissim, norem, odem, orem, ostrem, parkinsonism, salemme, salim, sephardim, solem, tatem, wasem, withem, yochim
Exim sounds like:
eachan, eagan, eagen, eagon, eaken, eakin, easom, eason, eckman, eckmann, ecogen, econ, economou, economy, ecumena, eczema, egan, eggen, eggum, egnew, egoism, egon, eichen, eichman, eichmann, eigen, eighmey, eighmy, eisaman, eischen, eiseman, eisemann, eisen, eisenman, eisenmann, eisin, eisman, eison, ekman, eocene, equine, equion, eschen, eschmann, esham, eskimo, eskin, esme, esmine, essen, essman, esson, eugene, eugenia, eugenie, eugenio, exam, examine, excision, exhume, exon, exum, exxon