Structural analysis of High-Level Petri Nets is a powerful technique, but it is less supported than in PNs. A symbolic calculus for Symmetric Nets (SNs) has been developed and implemented, which allows one to check structural properties directly on SNs without unfolding: however it is limited to a particular form of composition, restricted to functions that map to sets. To complete the calculus for more general applications the ability to solve the composition of general SN arc expressions in a symbolic way is required. In literature, a few papers show how to solve this operation for a restricted category of SN. In this paper, we formalize the algebraic composition of general SN bag-functions. Some applications are also discussed.