Relations between mental and physical aspects of an agent can be of various types. Sensing and acting are among the more commonly modelled types. In agent modelling approaches often this is the only interaction between the physical and mental; other possible types of interactions are abstracted away. If it is also taken into account that the agent's mind has a materialization in the form of a brain, the relations between mind and matter may become more complex. An explanation of a dynamic pattern may involve mental aspects, physical aspects, and interactions between mental and physical aspects. An explanatory perspective sometimes advocated for such more complex phenomena is explanatory pluralism. According to this perspective an explanation can consist of parts of a different signature, for example, a partial physical explanation and a partial mentalistic explanation. Each of these partial explanations is insufficient to explain the whole phenomenon, but together they do explain the whole, if some interaction is assumed. How for such explanations the different types of interaction between mind and matter of an agent and the material world can be modelled in a conceptually and semantically sound manner, and how the overall explanation is composed from the parts, using these interactions, is the main topic of this paper. The generic model presented can be used to model, explain and simulate a variety of phenomena in which multiple mind-matter interactions occur, including, for example, sensing and acting, (planned) birth and death, bacterial behaviour, getting brain damage, psychosomatic diseases and applications of direct brain-computer interfaces. © 2002 Elsevier Science Ltd. All rights reserved.