Awesome concept!

A few small bugs/oversights:

The final upgrade's cost scales downwards, I assume that was unintentional.

The tutorial resets every time you prestige. Seems unnecessary.

The complexity of trying to optimize the board becomes a little unfun in that pieces swaps are not remotely continuous, you can easilly x10 or /10 your setup by moving one piece one square; buying new things can actually worsen your best possible setup in a few cases; there don't seem to be many useful heuristics (even the ones encouraged by the upgrades themselves)--one board I would be pointing everything at a central rook, another time I would be blocking in all my pieces and pointing everything at an empty square, with very little understanding as to why one mechanic is better than the other in that instance; and if you do try to experiment, there's no way to save your best loadout, so you're as likely to forget it as not.

I can't imagine how this will scale with more multipliers, either it will be a total black box or there will be some factors introduced that trivialize the rest, and either way seems a little sad.

All that said, if you just forget about optimizing much and find a good enough setup and run with it, it's a lot of fun! I especially love how all the mechanics are faithful extensions of piece principles.