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Density functional theory calculations with an on-site Coulomb repulsion term reveal competing ground states in (111)-oriented (LaAlO(3))(M)/(SrTiO(3))(N) superlattices with n-type interfaces, ranging from spin, orbitally polarized (with selective e(g)('), a(1g), or d(xy) occupation), Dirac point Fermi surface, to charge-ordered flat band phases. These phases are steered by the interplay of (i) Hubbard U, (ii) SrTiO(3) quantum well thickness, and (iii) crystal field splitting tied to in-plane strain. In the honeycomb lattice bilayer N = 2 under tensile strain, inversion symmetry breaking drives the system from a ferromagnetic Dirac point (massless Weyl semimetal) to a charge-ordered multiferroic (ferromagnetic and ferroelectric) flat band massive (insulating) phase. With increasing SrTiO(3) quantum well thickness an insulator-to-metal transition occurs.