I am having difficulty modelling the effect of horizontal product differentiation between multiproduct firms. I've been looking at models specifically by Hotelling and d'Aspremont. Hotelling concluded that in duopolistic competition, an equilibrium was found through firms differentiating minimally, (i.e. designing products of similar attributes) whilst d’Aspremont shows the opposite with the equilibria resting at maximal product differentiation.
However, both of these principles do not take into account multiproduct firms, where firms could produce different varieties of the same product (take shoes for example) where some are highly differentiated and others may be similar to a competitor. Is there a model that explains this situation?