In this paper, we present a novel trajectory planning method for externally-actuated modular manipulators (EAMMs), consisting of multiple rotor-actuated links with joints that can be either locked or unlocked. This joint-locking feature allows effective balancing of the payload capacity and dexterity of the robot but significantly complicates the planning problem by introducing binary decision variables. To address this challenge, we leverage the problem’s intrinsic structure, i.e., the payload at the end-effector being enhanced by merely locking its immediate connected links; this allows us to break down the complex planning problem into a series of manageable subproblems and solve them sequentially. Our approach significantly reduces the problem’s complexity: in a serial n-link EAMM with m joint-lock mechanisms, where there could potentially be 2mdistinct configurational dynamics, we require solving only n + 1 trajectory optimization problems for single rigid body dynamics sequentially, thereby rendering the problem tractable. We substantiate the efficacy of our method through various simulation and experimental studies, covering ground-free and ground-bound configurations as well as both motion-only and manipulation tasks.