While balance would be a challenge, I think it would be feasible. The easier approach to this would be “strategy hosers” — parts that suck against everything but a specific strategy. You wouldn’t want to use those parts all the time because overall they’re bad, but if one strategy becomes overly dominant then they’re worth it.

Another thing may be to split parts in incompatible categories — like the five colors in Magic: the Gathering. The nifty thing in Magic is that each color has things it can’t handle on its own, they all have built-in weaknesses. That makes it really hard to find the one strategy that’s stronger than any other since other colors can take advantage of the color’s weakness to beat it. I’d have to think more about it, but I think an approach similar to this could work well.