The typical light airplane can PROBABLY be controlled after experiencing a failure of any one control axis (assuming that it is not jammed hard-over):

Pitch Failure: Use elevator trim, power, flaps. Worst case shift pax/cargo forward or aft. If the elevator cables break, the pitch trim should work fine (the elevator will move freely in response to trim). If the elevator is jammed, the trim will still provide some authority.

Aileron Failure: Use rudder to induce roll as needed.

Rudder Failure: Use aileron bank to control heading.

For the last two, you might have to fly uncoordinated and side-load the gear on landing but oh well.

Odds are very low that more than one axis would fail at the same time.