The norm-PRR method can be extended to handle stochastic constraints or more general composite structures beyond the finite-sum form by incorporating additional terms in the update rule that account for the stochastic nature of the constraints. One approach could be to introduce a regularization term that penalizes violations of the stochastic constraints, similar to how the weakly convex function φ penalizes deviations from the desired solution in the current formulation. By modifying the update rule to include terms that ensure compliance with the stochastic constraints, the norm-PRR method can be adapted to handle a wider range of optimization problems with stochastic elements.