Umpteen rhymes with:
augustin, canteen, cantin, casteen, chasteen, chretien, christine, cortine, eighteen, fifteen, foltene, fourteen, gelatine, guertin, justine, kristine, lopatin, martine, muntean, nineteen, o'steen, preteen, routine, seventeen, shasteen, sistine, sixteen, steen, stene, teen, thirteen, valentin