That's a good thought and the 'change up' concept I think would be important to creating value in various market conditions. As long as the data you fit all belonged to a similar market condition you could classify your strategies based on the larger market condition and search for which of your strategies fit best for now. Pretty cool foundation for automating ideas too and determining when each of your strategies would turn themselves on or off.
IMO:
Many confuse 'overfitting' with 'curvefitting.'
Curvefitting might be viable, if the 'fitting' lasts long enough, and;
the strategy can quickly recognize when the fit no longer exists, and can flow (in your case) to another instrument that does fit (or stop trading until the fit resumes).
Other systems will 'change up' the strategy into one (from its arsenal) that does fit, when the prior one stops 'fitting.'
