In the present work we describe all orthogonal systems consisting of three ternary quasigroup operations and of all (three) ternary selectors, admitting at least one nontrivial paratopy. In [11] we proved that there exist precisely 48 orthogonal systems of the considered form, admitting at least one paratopy, which components are three quasigroup operations, or two quasigroup operations and a selector. Now we show that there exist precisely 105 such systems, admitting at least one nontrivial paratopy which components are two selectors and a quasigroup operation, or three selectors.