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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) otimes 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)⊕ SO(N)] otimes C<sub>2</sub>, where C<sub>2</sub> is the symmetry group of the square

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