The effects of an off-diagonal quadratic symmetry-breaking field, g, on a three-component (n=3) cubic model with no accessible fixed points are studied. It is shown that this perturbation induces a crossover from first-order to continuous transition. Depending upon the initial values of the parameters characterizing the model, two types of (g,T) phase diagrams are possible, both of which are rather complex, exhibiting tricritical, critical, and critical end points. The (g,T) phase diagrams are studied using large-g expansion, mean-field theory, and renormalization-group analysis. A universal amplitude ratio associated with the critical end points is calculated to leading (zeroth) order in μ=4-d. The phase diagrams are predicted to be realizable in certain n=3 cubic crystals undergoing structural phase transitions, such as BaTiO3, RbCaF3, and KMnF3. © 1982 The American Physical Society.