Here's what rhymes with outdo.
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 taboo zoo adieu ado brew hu ku loo mu nu pew seu shu sou tattoo vu woo yew yu coo cou ewe feu gu ru shou thu tzu vou wou wu goo moo shoo gnu roux thew whew booboo into through few view grew que crew pursue threw flew q anew bamboo clue cue glue hue queue undue cu debut flue slew subdue undo flu piu thru beaucoup eschew fue hew mieux shrew sprue vnto vue clew mew outgrew redo strew spew zebu slue phew achoo screw canoe renew accrue ensue untrue jusqu overdue skew shampoo imbue overdo halloo valuer bugaboo endue indue kazoo peekaboo bestrew wazoo atishoo review hitherto residue withdrew avenue retinue caribou revue sinew askew ballyhoo cockatoo honeydew fondue foreknew marabou buckaroo muumuu overshoe prevue overdrew regrew interview revenue overview rendezvous construe overthrew barbecue kangaroo barbeque overflew superglue overgrew hullabaloo misconstrue