  The field-theoretical model describing multicritical phenomena with two
coupled order parameters with n_{||} and n_{\perp} components and of O(n_{||})
\oplus O(n_{\perp}) symmetry is considered. Conditions for realization of
different types of multicritical behaviour are studied within the
field-theoretical renormalization group approach. Surfaces separating stability
regions for certain types of multicritical behaviour in parametric space of
order parameter dimensions and space dimension d are calculated using the
two-loop renormalization group functions. Series for the order parameter
marginal dimensions that control the crossover between different universality
classes are extracted up to the fourth order in \varepsilon=4-d and to the
fifth order in a pseudo-\varepsilon parameter using the known high-order
perturbative expansions for isotropic and cubic models. Special attention is
paid to a particular case of O(1) \oplus O(2) symmetric model relevant for
description of anisotropic antiferromagnets in an external magnetic field.
