The Resource-Constrained Project Scheduling Problem (RCPSP) is a general problem class of scheduling problems. It even contains the well-known job shop scheduling problem as a special case. In these problems, jobs demand different amounts from multiple resources at once. The goal is to minimize completion time while satisfying resource capacity constraints throughout the schedule. The RCPSP has several variations and generalizations, one of which is the multi-mode problem. Multiple operation modes are given for jobs, differing in resource usages and execution times. Another generalization is where resources have time-varying capacities instead of a constant limit. The S-graph framework was developed for batch process scheduling and used successfully in various applications. The advantages of this approach motivate research to extend its capabilities to more general problem classes and apply it in various specialized case studies. The authors have previously presented an extension of the S-graph framework for RCPSP and its multi-mode generalization. In this work, a further extension is proposed for handling time-varying capacities. The method relies on a model transformation technique and recent algorithmic developments of the framework.