A possible mechanism for the spin transitions in various stacking conformations of bis(phenylmethylenyl)-[2.2]paracyclophanes, which have close-lying lowest singlet, triplet, and quintet spin states, is theoretically investigated by using diphenylcarbene dimers as models. Spin-orbit coupling (SOC) matrix elements, which play an essential role in the spin transition phenomena, are calculated with the effective one-electron spin-orbit Hamiltonian. The SOC between the first excited singlet state and the first excited triplet state and that between the first excited triplet state and the lowest quintet state are strong. The SOC between the first excited quintet state and the first excited triplet state and that between the first excited triplet state and the lowest singlet state are also strong. These results demonstrate that the spin conversion between the low-spin singlet state and the high-spin quintet state can occur via the first excited intermediate-spin triplet state. We propose that possible photoinduced spin-crossover phenomena can be observed in these organic molecular systems.