We present here an extension of the monomer transition density approach to spin multiplicity-altering excitation energy transfer (EET) processes. It builds upon complex-valued wave functions of the density functional theory-based multireference spin-orbit coupling configuration interaction method for generating the one-particle transition density matrices of the donor and acceptor molecules, which are then contracted with two-electron Coulomb and exchange integrals of the dimer. Due to the extensive use of symmetry relations between tensor components, the computation of triplet-singlet coupling remains technically feasible. As a proof-of-principle application, we have chosen an EET system, consisting of the phosphorescent platinum complex AG97 as the donor and the fluorescein derivative FITC as the acceptor. Taking experimental conditions into account, we estimate a Förster radius of about 35 Å. For intermolecular donor-acceptor separations close to the Förster radius and beyond, the error introduced by the ideal dipole approximation is rather small.