Maybe modify the screen's line[] pointers to point elsewhere while
switched away, and also the pointers of any of its
sub-bitmaps? I don't
know if it would work, and it would be hairy. Maybe it's being done
somewhere already.
And I *think* some of the asm blitters compute the difference between
two lines pointers and use this, probably to deduce the location of
other lines, so care would have to be taken if this is true (I very
vaguely remember something about that, but I'm afraid I can't be
more specific).