Here's what rhymes with mulatoo.
to do two too due du dew tu chew deux bu ju jus peu pu boo chou chu doo tue pooh poo who you new true knew blue drew u blew coup qu shoe zu lieu shew su sue vous fu lu rue stew zoo adieu ado brew hu ku loo mu nu pew seu shu sou vu woo yew yu coo cou ewe feu gu ru shou thu tzu vou wou wu goo moo redo shoo gnu roux thew whew achoo into through few view grew que crew pursue threw flew q anew clue cue glue hue queue renew undue cu debut flue slew taboo undo flu piu tattoo thru beaucoup eschew fue hew mieux outdo shrew sprue vnto vue clew mew strew spew zebu marabou slue phew booboo review residue screw bamboo canoe accrue ensue retinue subdue untrue caribou jusqu overdue skew revue shampoo askew imbue outgrew overdo halloo honeydew valuer bugaboo endue indue kazoo wazoo regrew atishoo revenue hitherto withdrew avenue rendezvous construe sinew ballyhoo cockatoo hullabaloo fondue foreknew peekaboo bestrew buckaroo muumuu overshoe prevue overdrew interview overview overthrew kangaroo overflew superglue overgrew barbecue misconstrue barbeque