Direct decompositions of $\omega$-foliated fitting classes of multioperator $t$-groups

Studying direct decompositions for the Fitting classes of multioperator $T$-groups, we establish that the direct sum of $n$-multiply $\Omega$-foliated Fitting classes of $T$-groups with right direction is also an $n$-multiply $\Omega$-foliated Fitting class with right direction, and the converse holds for some right directions: free, canonical, etc.