I have flown the US-Army version of the 172 the "T-41 Mescalero" this has 210hp engine & VP prop & balloon tyres. (Las-Vegas North Terminal)
Also built in France as the Reims Rocket. I flew one recently.
The FAA Type Certificate Data Sheet describes out what can be done within its constraints of the approved Type. STC's then add another set of possibilities. Will take a fair bit of research.
http://www.airweb.faa.gov/Regulatory...$FILE/3A12.pdf