We study the conditions under which the critical behaviour of the three-dimensional mn-vector model does not belong to the spherically symmetrical universality class. In the calculations, we rely on the field-theoretical re-normalization group approach in different regularization schemes adjusted by resummation and extended analysis of the series for renormalization-group functions. We address the question why the renormalization-group perturbation theory expansions available for the model with a record (six loop) accuracy have not allowed so far for a definite answer about the universality class for certain particular values of dimensions m, n. We show that an analysis based on the marginal dimensions rather than on the stability exponents leads to the robust results about the phase diagram of the model.