Agent-based modelling constitutes a versatile approach to representing and simulating complex systems. Studying large-scale systems is challenging because of the computational time required for the simulation runs: scaling is at least linear in system size (number of agents). Given the inherently modular nature of MABSs, parallel computing is a natural approach to overcoming this challenge. However, because of the shared information and communication between agents, parellelization is not simple. We present a protocol for shared-memory, parallel execution of MABSs. This approach is useful for models that can be formulated in terms of sequential computations, and that involve updates that are localized, in the sense of involving small numbers of agents. The protocol has a bottom-up and asynchronous nature, allowing it to deal with heterogeneous computation in an adaptive, yet graceful manner. We illustrate the potential performance gains on exemplar cultural dynamics and disease spreading MABSs.