  We analyze, in exact terms, multiband 2D itinerant correlated fermionic
systems with many-body spin-orbit interactions, and in-plane external magnetic
fields. Even if such systems with broad applicability in leading technologies
are non-integrable, we set up an exact solution procedure for them, which is
described in detail. Casting the Hamiltonian in positive semidefinite form, the
technique leads to the ground state and also characterizes the low lying
excitation spectrum.
