Molecules with identical nuclei exist in nature in the form of nuclear spin isomers. In general, spin isomers are not the eigenstates of total molecular Hamiltonian. It also contains parts able to transform spin isomers one into another. Recently, nuclear spin isomers relaxation induced by such a quantum mixing was successfully demonstrated in experiment. That motivates the search for general intramolecular interactions able to mix spin isomers. In the work, the general forms of the possible mixing interactions are found for C3v-type of molecules using generalized Jordan-Schwinger approach to the theory of quantum angular momentum.