While all tires with crown to some degree given a high enough pressure, not all tires will crown with reasonable pressures.
My truck tires will crown in a heartbeat. My Prius tires stay flat even at 45psi. They raise up and show that the side of the tread is not touching the ground, but they remain flat across the tire. It's easy to see how your tires are doing simply by looking at the tire. What's contacting shows dirt/dust. What touches the road in corners shows wear.
Be advised, however, that on some tires on some cars, wet traction and other low traction events can be problematic with overpressured tires. Try increasing psi's and monitor handling and tire wear patterns closely.
My inflation plate says 32psi, IIRC. I have them at 40 front and 37 rear. I monitor treadwear and the handling is fine.
As with all things, pay attention, get educated, and think things through.