Interacting N-vector order parameters with O(N) symmetry

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 have a multicritical transition with enlarged symmetry controlled by the chiral O(2) circle times O(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) circle times SO(N)] circle times C-2, where C-2 is the symmetry group of the square.