The matrix-form kinetic formalism developed earlier for multistage chemical reactions is generalized to the case of reactants with internal quantum quasiresonant states. Such internal quantum states may arise due to spins of the unpaired electrons of radicals or nuclear spins. The formalism gives an infinite hierarchy for matrix correlation patterns that can be truncated in two different ways. The simplest one reproduces the conventional integral encounter theory (IET). The second way results in the generalized modified encounter theory (MET). In the spinless problems such as intermolecular energy transfer MET is known to improve the results obtained with other methods. Thus we believe that the generalized MET taking account of all binary contributions will have wider applicability range than the conventional IET.