So how do you manage your banking and tax issues without going insane? Is your company providing you with high-quality tax advisors that help you deal with this issue?
It's not that complicated if you are just earning salary / self-employed income in places. GP's situation with those three countries -- given their fairly sane tax systems and streamlined reporting -- is probably about as complicated as an American's tax, especially if you have multiple states involved.
From my limited knowledge, companies do tend to handle the tax work for expats. In fact years ago when I was interviewing for an international position where I'd have been moving around a lot, as I recall, they told us something like they'd take some fixed percentage off our paychecks and handle the whole thing.
If you're on your own, you presumably have to hire an appropriate accountant.
This comes up even internally in the US if you're spending a lot of time in a number of states as a non-resident.