Engineers of embedded software systems rely on efficient design techniques and tools along with efficient run-time support. In the design of complex embedded real-time systems, the Hierarchical Scheduling Framework (HSF) has been introduced as a design-time framework enabling compositional schedulability analysis of embedded software systems with real-time properties. Moreover, the HSF provides a run-time framework guaranteeing that these nonfunctional requirements are met. In this paper a system consists of a number of semi-independent components called subsystems, and these subsystems are allowed to share logical resources. The HSF makes sure that the individual subsystems respect their allocated CPU budgets. However, as semi-independent subsystems share logical resources, extra complexity is introduced. Specifically, the contribution of this paper is a novel method to allow for budget overruns; a common scenario when a subsystem utilizes shared logical resources. This proposed method is not only more resource efficient than existing methods, but it is also more appropriate for supporting composability of independently developed real-time subsystems.