When analyzing or optimizing structures subjected to random vibrations, inherent uncertainties such as material properties may have a significant effect on the structural dynamic response. Therefore, these sources of uncertainty, together with the randomness of the applied loads, must be accounted for when performing stochastic optimization in order to ensure reliable structural designs. Probabilistic constraints related to first-passage failure and fatigue estimates under random vibrations depend on the computation of root mean square (RMS) responses, such as stress RMS responses. These quantities are typically difficult to compute for complex problems involving finite element analyses. The difficulty is further increased by the need for repeated function evaluations within an optimization process, which can lead to a substantial computational burden. In a recent study, these challenges were mitigated by using Gaussian process surrogate models for failure rates in combination with a dedicated adaptive sampling scheme to efficiently estimate RMS responses. Probabilistic constraints related to first-passage failure were evaluated using established results from random vibration theory, while inherent system uncertainties were propagated to compute the total probability of first passage. However, as the number of failure modes increases, the number of required surrogate models and the associated computational cost due to expensive function evaluations can grow significantly. To overcome this limitation, the present work proposes an adaptive classification-based approach that employs a Support Vector Machine (SVM) to approximate the failure domain defined by multiple failure modes or limit state functions. Reformulating the optimization problem from regression to classification enables a substantial reduction in the number of function evaluations, since not all failure modes or probabilistic constraints must be evaluated at every point in the design space. An adaptive sampling strategy based on a Generalized Max–Min scheme is used to refine the SVM and improve the approximation of the failure domain. The proposed methodology is applied to the stochastic optimization of a cantilever beam with a tip mass and a launcher payload adapter subjected to prescribed random excitations defined through power spectral densities.