Single Comment

Thank you for the comment, Daniil. I'll disagree with you to a slight
extent, but it's a matter of interpretation, not effect. Alice is
3-dimensional, even if that '3D' effect is achieved by adding 2D and 1D,
a gimmick 3D if you will, rather than allowing full 3D freedom on the
board. And Directed Alice, which allows a choice of which other 2D board to
go to, is 'more fully 3D' than Alice itself is. The switching between
boards gives greater freedom of movement than just moving on separate 2D
boards alone does. But as I said, it's more semantics than physics.

I have considered games similar to what you've suggested here, but not in
a chess context, and not much* recently [say the last 30 years.] I've gone
to simpler boards over the years - the games are easier to design. ;-)
Others have, however. One step toward what you discussed is Chess on the Rainbows.
http://www.chessvariants.org/index/msdisplay.php?itemid=MPchessontherain

*Did design a 4D wargame with an option of a small 5D 'transfer board'
that's connected to all the other 'levels/2D boards'. And each 2D board
has terrain, hills, trees, towns, with elevation and blocking rules that
apply acroos the levels, so that kinda adds another dimension...