The BDI architecture, where agents are modelled based on their belief, desires, and intentions, provides a practical approach to developing intelligent agents. One of the key features of BDI agents is that they are able to pursue multiple intentions in parallel, i.e. in an interleaved manner. Most of the previous works have enabled BDI agents to avoid negative interactions between intentions to ensure the correct execution. However, to avoid execution inefficiencies, BDI agents should also capitalise on positive interactions between intentions. In this paper, we provide a theoretical framework where first-principles planning (FPP) is employed to manage the intention interleaving in an automated fashion. Our FPP approach not only guarantees the achievability of intentions, but also discovers and exploits potential common sub-intentions to reduce the overall cost of intention execution. Our results show that our approach is both theoretically sound and practically feasible. The effectiveness evaluation in a manufacturing scenario shows that our approach can significantly reduce the total number of actions by merging common sub-intentions, while still accomplishing all intentions.