Using classifier's probabilities as independent variables to predict Y
This is called "stacked ensembling," or just "stacking."

Wikipedia

I'm not aware of any theoretical mathematical support, but intuitively it may smooth out the results of the $r$ initial models, possibly (depending on the final model) promoting models on data segments where they perform best.  Stacking consistently wins Kaggle competitions, though the added complexity might make it less attractive for certain applications.