  Sums of matrix elements of spin-dependent two-body momentum-independent
interactions and sums of their products are calculated analytically in the
basis of many-body states with given total spin --- the states built from spin
and spatial wavefunctions belonging to multidimensional irreducible
representations of the symmetric group, unless the total spin has the maximal
allowed value. As in the first part of the series [V. A. Yurovsky, Phys. Rev. A
91, 053601 (2015)], the sum dependence on the many-body states is given by
universal factors, which are independent of the Hamiltonians of non-interacting
particles. The sum rules are applied to perturbative analysis of energy spectra
and to calculation of two-body spin-dependent local correlations.
