A 2D anisotropic system of S = 1 centers of the charge triplet type in systems with variable valence or “semi-hard-core” boson systems with a limitation for the occupation of lattice sites n = 0, 1, 2 is studied in the framework of the pseudospin formalism. Assuming that the ground state is a quantum paramagnet, the pseudo-spin wave spectrum and also the conditions of the condensation of pseudomagnons with a phase transition to a superconducting state have been found using the Schwinger boson method.