  We consider the critical behavior of the most general system of two N-vector
order parameters that is O(N) invariant. We show that it may a have a
multicritical transition with enlarged symmetry controlled by the chiral
O(2)xO(N) fixed point. For N=2, 3, 4, if the system is also invariant under the
exchange of the two order parameters and under independent parity
transformations, one may observe a critical transition controlled by a fixed
point belonging to the mn model. Also in this case there is a symmetry
enlargement at the transition, the symmetry being [SO(N)+SO(N)]xC_2, where C_2
is the symmetry group of the square.
