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Abstract We explore the phase diagram for an SU(N) gauge theory in $$2 + 1$$ 2+1 dimensions with three families of fermions with different masses, all in the fundamental representation. The phase diagram is three dimensional and contains cuboid, planar and linear quantum regions, depending on the values of the fermionic masses. Among other checks, we consider the consistency with boson/fermion dualities and verify the reduction of the phase diagram to the one and two-family diagrams.