Bayesian Model Averaging with a finite set of models coming from different spaces (classes)

I have L Latent Dirichlet allocation models (different #topics), K mixture of dirichlet models (different #centers) and N counting grid models (different Grid/Window size). K,L and N is finite (= ~10).

I must perform classification on some BOW data.

Intuition says that different classes are better modeled by different models and I wanted to figure out a way to select/average the model for each class.

Does anyone know if it is possible? Anyone attempted it? Suggestions?