On a 2002 A4 quattro, two right side tires (directional tires!) need replaced - one leaking from a crack in the sidewall and the other was punctured too close to the sidewall. Remaining left side tires are still good with 60% or so tread remaining. Question is can I get away with just 2 new tires and OK to just mount on the right? Or remount one of the remaining tires and put the 2 new ones on the same axle? Or am I gonna need 4 new tires?

On a 2002 A4 quattro, two right side tires (directional tires!) need replaced - one leaking from a crack in the sidewall and the other was punctured too close to the sidewall. Remaining left side tires are still good with 60% or so tread remaining. Question is can I get away with just 2 new tires and OK to just mount on the right? Or remount one of the remaining tires and put the 2 new ones on the same axle? Or am I gonna need 4 new tires?
You will need to get four new tires or you can have two new tires shaved to match the diameter of the existing tires. Tire Rack and Discount Tire will do this for you. You need to measure the actual tread depth in the existing tires for this to be done.

If you do not do this the diff can wear out prematurely

You can get away with two, but the two new ones can not be mounted on the right side without shaving them down. I recommend getting all 4 if you have the funds. If not, get two and mount them on the rear and move the rear left tire (used one) to the right side. This requires dismounting the tire from the rim and flipping it around since it is directional.

You can get away with two, but the two new ones can not be mounted on the right side without shaving them down. I recommend getting all 4 if you have the funds. If not, get two and mount them on the rear and move the rear left tire (used one) to the right side. This requires dismounting the tire from the rim and flipping it around since it is directional.
Only after shaving