Systems described by an O(n) symmetrical φ⁴ Hamiltonian areconsidered in ad-dimensional film geometry at their bulk critical points. Adetailed renormalization group (RG) study of the critical Casimir forces induced between the film’s boundary planes B_j,j = 1,2, by thermal fluctuations ispresented for the case where the O(n) symmetry remains unbroken by the surfaces. The boundary planes are assumed to cause short-range disturbancesof the interactions that can be modelled by standard surface contributions ∝φ² corresponding to subcritical or critical enhancement of the surface interactions. This translates into mesoscopic boundary conditions of the genericsymmetry-preserving Robin type ∂_nφ= ̊c_jφ. RG-improved perturbation theory and Abel–Plana techniques are used to compute the L-dependent part f_res of the reduced excess free energy per film area A → ∞ to two-loop order. When d < 4, it takes the scaling form f_res ≈ D(c₁L^Φ/ν,c₂L^Φ/ν)/L^d−1 as L → ∞, where c_i are scaling fields associated with the surface-enhancement variables c˚_i, while Φ is a standard surface crossover exponent. The scaling function D(c₁,c₂) and its analogue for the Casimir force are determined via expansion in  = 4 − d and extrapolated to d = 3 dimensions. In the special case c₁ = c₂ = 0, the expansion becomes fractional. Consistency with the known fractional expansions of D(0,0) and to order ^3/2 is achieved by appropriate reorganization of RG-improved perturbation theory. For appropriate choices of c₁ and c₂, the Casimir forces can have either sign. Furthermore, crossovers from attraction to repulsion and vice versa may occur as L increases.