Conditional autoregressive distributions are commonly used to model spatial dependence between nearby geographic units in disease mapping studies. These distributions induce spatial dependence by means of a spatial weights matrix that quantifies the strength of dependence between any two neighboring spatial units. The most common procedure for defining that spatial weights matrix is using an adjacency criterion. In that case, all pairs of spatial units with adjacent borders are given the same weight (typically 1) and the remaining non-adjacent units are assigned a weight of 0. However, assuming all spatial neighbors in a model to be equally influential could be possibly a too rigid or inappropriate assumption. In this paper, we propose several adaptive conditional autoregressive distributions in which the spatial weights for adjacent areas are random variables, and we discuss their use in spatial disease mapping models. We will introduce our proposal in a multivariate context so that the spatial dependence structure between spatial units is shared and estimated from a sufficiently large set of mortality causes. As we will see, this is a key aspect for making inference on the spatial dependence structure. We show that our adaptive modeling proposal provides more flexible and accurate mortality risk estimates than traditional proposals in which spatial weights for neighboring areas are fixed to a common value.