Balanchine's rhymes with:
alkenes, amphetamines, argentines, arlene's, bernstein's, bylines, caesareans, calgene's, carotenes, engines', eritreans, evergreens, feldstein's, finkelstein's, gabardines, hammerstein's, josephine's, libertines, limousines, listerines, magazine's, magazines, magazines', mangosteens, newsmagazines, nicotine's, opalines, peregrines, philippines, philippines', philistines, protein's, proteins, quarantines, seventeens, soybeans, springsteen's, submarine's, submarines, tangerines, thirteen's, vitarine's
Balanchine's sounds like:
balancing, belonging, belongings, blanking, blinking