A model is presented to study the (weak) interaction between two conical intersections (e.g., a dimer of two loosely bound molecules each characterized by a conical intersection). The model is an extension of a previous model for a single conical intersection formed by an electron housed by a vibrating molecule [Baer and Englman, Mol. Phys. 75, 293 (1992)]. The main result of this study is that the intermolecular coupling removes part of the degeneracy of the global system and in turn forms a new degeneracy, but will not affect the multivaluedness of the nuclear wave functions.