I received a mpc today - used - and the shank is an little out of round.

How much can you get back into round?

Totally depends. Sometimes you can't tell, sometimes it's never right again.

You can get it pretty close to perfect, but not with just "the tool". The collars that Instrument Innovations sell are a good way for the band director to avoid overshooting and flaring the end, but if you're trying harder it's more a case of using loose mandrels and working the high spots from the outside.

If the backbore ends with a single taper, with a flat edge to the shank end, then you can usually get it very very close. It's harder to camouflage the exterior damage when there's an extra chamfer/countersink at the backbore exit.

The original damage is almost always repairable... other people's repair attempts, less so.

^^^

This.

You have to remember that it's not a true cylinder you're dealing with. That makes it harder. And the chamfer/countersink issue may be ultimately insurmountable -- even with a lot more equipment than you're unlikely to see outside a real machine shop. Even then, ... :( I have one where I've decided "close enough is good enough".