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Cluster-weighted factor analyzers  (CWFA) models are a flexible family of mixture models for fitting the joint distribution of a random vector constituted by a response variable and a set of explanatory variables. It is a useful tool especially when high-dimensionality and multicollinearity occurs.This paper extends CWFA models in two significant ways. Firstly, it allows to predict more than one response variable accounting for their potential interactions. Secondly, it identifies factors that relate to disjoint clusters of explanatory variables, simplifying their interpretatiblity. This leads to the multivariate cluster-weighted disjoint factor analyzers (MCWDFA) model. An alternating expectation-conditional maximization algorithm is used for parameter estimation. Application of the proposed approach to both simulated and real datasets is presented.