This paper introduces an agent framework that integrates the Belief, Desire, Intention (BDI) model with Multi-Context Systems (MCS), particularly for dealing with diverse knowledge sources in belief revision, deliberation and means-end reasoning. By specifying a separate MCS in each BDI-component, the framework manages the interaction between, possibly conflicting, sets of beliefs, desires, intentions and plans generated by specialized sub-systems. A MCS-based BDI-component generates an equilibrium. An approach is introduced for transferring equilibrium between MCSs according to the BDI control loop. This involves the translation of knowledge bases to Answer Set Programming (ASP) to build a shared logic. The proposed framework contributes to the advancement of hybrid intentional agents, where multiple goals and plans must be interwoven in order to deal with a complex multi-modal domain. The potential of the framework is illustrated in a running example, where a driving assistant agent is designed to manage diverse mental states of a human driver, such as emotions, motivations and norms, within each stage of the BDI control loop, producing a plan that is in balance with the diverse contexts.