Bass distortion before tweeter distortion with a monitor at high volume?

" My understanding is that I would want to high-pass the bass on the speaker before it reaches the point of distortion, solving that issue. "

Its not so much a distortion issue. You're just letting a different part of the system handle certain frequencies. That said, you can make just about anything distort if you push it hard enough. If you don't install a sub, that doesn't mean the lows are going to distort. If its a small speaker, its just not able to reproduce really low notes.

" To restate the question: With a high quality monitor, is it safe to say that the tweeter can play at higher volume without distorting compared to the woofer? "

No. At least for the most part. If your amp is struggling to drive a whole speaker and you use it just for the highs, you may be able to get more volume.

Here's a link to a very good article on subs, and everything you need to do for best results. No stone is left upturned, and its written so that anyone can follow it. You don't need years of experience to understand it.
http://vandersteen.com/media/files/APJ%20Files/APJ_2_rl.pdf

" Here is what I don't understand. If I try to play a small speaker in a too large room and have to supply too much power to it, it will distort. True? It just can't play that loudly."

That's true.

" So simply adding the subwoofer would not relieve the "strain" on the drivers, it would only provide more bass, but I would still have to live with the distortion, both from the woofer and from the tweeter (I'm talking about a two-way speaker)."

True again.

" If I did relieve the speaker of much of the bass load with a high pass filter, you are saying that you believe in most cases the part of the signal that goes to the main speaker would still be distorted? "

It depends. There's several variables at play. If your amp wasn't straining to begin with, then you should still hear the distortion. A speaker can only play so loud. If removing some of the bass frequencies helps an amp that's being driven too hard, then you may be able to squeeze more volume out of the system.

That said, this is usually not an issue for your typical high end system. Most audiophiles are far more concerned with sound quality than volume. When an audiophile is looking for volume, it usually means something's wrong. When a system is sounding good, most people don't feel the need for loud music.

Your original theory, for the most part, is correct. Removing the low frequencies should allow a speaker to play louder, but its usually not a tactic used in high end systems. It's done all the time in car systems and pro installs like a night club.

" The point of this thread is to discuss whether that distortion, which most seem to agree would occur on the bottom end first, could be relieved by high passing and allowing the sub to take the lowest range."

That's not true. If you have to push an amp hard to drive your speakers, the highs will be more of a problem. And in reality, this is far more likely to happen.

If you have a Bryston 4, you're correct in thinking that it will be able to handle almost any small speaker with ease. But that doesn't solve the problem. There's 2 things you need to consider.Regardless of what happens with bass, all speakers are different. Some may be able to play loud enough for you, while others can't. It has to be taken on a case by case basis, and not generalize.

More importantly, If you have a small speaker, the sub will almost certainty not be able bridge the gap between sub frequencies and the lowest frequencies the small speakers put out. Using an xover to cut out the lowest frequencies in the small speaker is only going to make the problem worse. I think this is where the confusion is coming from. Subwoofers are not woofers. They are not meant to play low frequencies, they're meant to play sub frequencies. The right way to do this would be to use a sub with full range speakers. That way, everything is doing what they were designed to do.