Bioengineering rhymes with:
reengineering, engineering, reengineering, engineering, imagineering, reengineering, auctioneering, domineering, electioneering, engineering, imagineering, oceaneering, pioneering, reengineering
reengineering, engineering, reengineering, engineering, imagineering, reengineering, auctioneering, domineering, electioneering, engineering, imagineering, oceaneering, pioneering, reengineering