Recently, it was shown that a radial basis function network (RBFN) with a softmax output layer amounts to pooling by Dempster's rule positive and negative evidence for each class, and approximating the resulting belief function by a probability distribution using the plausibility transform. This so-called latent belief function offers a richer uncertainty quantification than the probabilistic output of the RBFN. In this paper, we show that there exists actually a set of latent belief functions for a RBFN. This set is obtained by considering all possible dependence structures, which are described by correlations, between the positive and negative evidence for each class. Furthermore, we show that performance can be enhanced by optimizing the correlations brought to light.