To what extent is it okay to rewrite, adapt, or otherwise change classical plays to suit ones’ purpose?

it depends on what you mean, if you mean ripping off a play for a school production then do whatever, but once it gets big you probably have to pay royalties or stick to ceratin guideleines set by the writers

Not for a classical play. But is it fair to the playwright?

Well, if the playwright is dead and the copyrights are expired, you aren't hurting anyone. So long as you make it clear that you are presenting an adaptation of the original work, I don't see any problem with it.

It's fairly common practice to edit plays. Different actors have different styles and different emphasis on different parts. I saw an episode of antiques road show (I'm not a play guy, so my knowledge is fairly weak) where someone brought in some John Barrymore memorabilia. One of the things was a script for a shakespearean play. King Lear, I believe it was. It was edited in John Barrymore's hand, with some passages scribbled out and others changed a bit here and there. It was the appraiser who said it was common practice to do such.

The book was fairly valuable, don't recall exactly how much. And as an interesting aside, Barrymore never played Lear. He always wanted to but never had the chance.

As to how fair it would be to the playwright, I imagine that it depends on the playwright. I doubt if Shakespeare would have minded much. But, I could be wrong. Never cared much for his work, myself. Wasn't he basically a hack when he was alive? Playing for the common man? It's amusing how intellectual his work is seen today. In it's day it was raunchy stuff.