If you look at the great leaps and bounds that piston engined aircraft made from the beginning of WW 2 till the end. What could have happened if you delayed development of jet aircraft 10 to 15 years ? More use of counter rotating props, swept wings, bigger more powerful engines. Are speeds of 500 mph and above possible.
AFAIK the physics of prop-driven aircrafts mean that practical max speed would probably not be much higher than 500mph even with very powerful engines, and swept wings which are useful in transonic flight may also not be very beneficial or practical here (but well, B-36, turboprop Voodoo and Tu-95 exist).
If jet engines and turboprops are out of the picture, piston engines would probably converge towards fuel-injected designs with multistage turbochargers or more likely turbocompound designs, with better utilization of space than most WW2 engines (that is closer to Griffon than Merlin), and very high quality fuel.
Speed would be capped, but increases in power density could allow notable increases in fuel efficiency, aircraft mass and payload to obtain increased range, better avionics and heavier armament. Twin engine aircrafts might become more important than they were in WW2 as they would have the mass and space for particular weapons, turbocharging arrangements and avionics. Single-engine aircrafts may remain relevant at certain altitudes and roles however. Armament could be improved and streamlined with the generalization of revolver, gatling or Gast autocannons, until missiles become available.