Hey, Jeremy. There are several ways to deal with directionality. Gary Gifford designed a delightful game with directional pawns represented by a spear and shield. A slightly smaller, slightly offset icon with a directional arrow should work quite nicely for a 1-directional knight, for example. You'd have a rather trying time stacking 3-4 of these different pieces, though. Probably have to do something like Navia Drapt and use a marked grid to show moves, which sort of makes the original concept disappear. Or use an alphanumeric system to indicate piece components and directionality. You might also make a board with oversized squares so you could use oversized icons that can carry more info. 

You're also venturing into the realm of the 'build it yourself' armies that were often an outgrowth of role-playing games or wargames, or both. I'm sure someone could tell you names, but I've seen a few build-it games in the CVPages. Most of them appear to be exceedingly long and complex, whether they are or not, so may not have gotten a lot of play.

I'd playtest 2 and 3 part compounds before trying to create 'Mutant Monster Chess' with its '2 to the n' piece possibilities [if not more]. But that's just me; being lazy, I'd raid the icon list for things like berolina pawns and sergeants to show stacks of 2 or 3 pawns, for example. There's enough pieces to cover most 2, 3, and some 4 part compounds. That'd give me enough to experiment with for a while, and indicate what I thought could be reasonably done next. 

I also believe there's a limit to the number of different pieces you can put into a game, no matter the board size, total number of pieces, or complexity of movement rules. I probably came very close to, or [far] more likely went past it in Fortress Chess, trying to do too many things at once. People don't play those games. That's a reason for not doing a game. I generally get better results when things come out of a game idea than if more ideas get put in. Those games, stuffed with ideas, can lack clarity, much like me, when I write things like this, but ramble on. ;-)