Several distinct classes of unitary mode transformations have been known to exhibit the strict suppression of a large set of transmission events, as a consequence of totally destructive many-particle interference. In another work [C. Dittel et al., Phys. Rev. Lett. 120, 240404 (2018)] we unite these cases by identifying a general class of unitary matrices which exhibit such interferences. Here we provide a detailed theoretical analysis that substantially expands on all aspects of this generalization: We prove the suppression laws put forward in our other paper, establish how they interrelate with forbidden single-particle transitions, show how all suppression laws hitherto known can be retrieved from our general formalism, and discuss striking differences between bosons and fermions. Furthermore, beyond many-particle Fock states on input, we consider arbitrary pure initial states and derive suppression laws which stem from the wave function's permutation symmetry alone. Finally, we identify conditions for totally destructive interference to persist when the involved particles become partially distinguishable.