Regime classification pre model training?
Just a couple thoughts:


It looks like these "regimes" could be represented as a latent variable:  you could probably design a bayesian model in which the OLS model depends on the value of this latent variable. This means that the model would still be trained only with the observed features, but would internally predict the value of the regime and this value would determine the parameters of the OLS model. 
A more direct approach for this kind of case-by-case setting would be to use decision trees (or random forests), since they can handle independent models in different branches. However I'm not sure how to make decision trees and linear regression work together (or if it's possible at all).