Hierarchical interface-based supervisory control (HISC) decomposes a discrete-event system into a high-level subsystem, which communicates with n 1 low-level subsystems, through separate interfaces that restrict the interaction of the subsystems. It provides a set of local conditions that can be used to verify global conditions such as nonblocking and controllability. As each clause of the definition can be verified using a single subsystem, the complete system model never needs to be stored in memory or traversed, offering potentially significant savings in computational resources. In this article, we extend the range of the behaviour of low-levels that interfaces can model by adding a new type of event, low data events and by relaxing some restrictions in the HISC definitions. This allows us to (i) request events that do not need to be followed by an answer event, (ii) start a low-level on a task and then poll it for completion, (iii) be able to send additional commands while a low-level is already processing a command (iv) model low-levels that behave as buffers and (v) allow unsolicited information (status, etc.) to be sent up from a low-level. Besides greatly enriching the behaviour that can be modelled as interfaces and thus expanding the systems that HISC can effectively be applied to, the changes can enable behaviour to be moved from the high-level to the low-levels. We demonstrate this when we discuss the application of our method to a large manufacturing system example based upon the AIP example, where we saw a 3.4 times reduction in computation time and a 6.5 times reduction in memory use. This helps prevent the high-level from growing too large, allowing the HISC method to apply to larger systems.