  Perturbing the standard Gross-Neveu model for $N^3$ fermions by quartic
interactions with the appropriate tensorial contraction patterns, we reduce the
original $U(N^3)$ symmetry to either $U(N)\times U(N^2)$ or $U(N)\times
U(N)\times U(N)$. In the large-$N$ limit, we show that in three dimensions such
models admit new ultraviolet fixed points with reduced symmetry, besides the
well-known one with maximal symmetry. The phase diagram notably presents a new
phase with spontaneous symmetry breaking of one $U(N)$ component of the
symmetry group.
