Bioengineer rhymes with:
reengineer, engineer, reengineer, engineer, imagineer, reengineer, auctioneer, conventioneer, domineer, electioneer, engineer, imagineer, lanier, mutineer, pioneer, reengineer, souvenir, veneer, wagoneer
Bioengineer sounds like:
bancomer, bensenyore, bingenheimer, bonsignore