I have an 87 caprice classic, what would be the largest tire size I could fit on it without altering ride height? Would 275/60r15's fit on the rear with no problems or is that too big? Thanks.

I've used 255/60r15's on my '88 9C1 with no problems - 275s will require an 8" wheel. You should not have clearance problems in the rear with them, but you will need to recalibrate your speedo.

FWIW, I find that I get better economy with the stock sized 225/70R15s that I have on it now. I don't notice a big difference in handling, either. With the 225s, I find I can still blaze a 25MPH sweeping freeway transition ramp, noisily, at 60.

The 255s had so much stick to them that I was wearing them out fast.

On an 8 inch wheel, 275/60s will fit fine on the rear. At least it does on my 89.

will the 275/60/15's stick out of the wheel well?

Not with a 4" backspacing.