Here's what rhymes with impodible.
erodible Words that almost rhyme with impodible
potable notable approachable quotable inapproachable irreproachable unapproachable reproachable knowable sociable emotional disposable negotiable unknowable notional unsociable devotional controllable revokable consolable promotional inconsolable unemotional nonnegotiable renegotiable uncontrollable overemotional