We study the problem of control synthesis for multi-agent systems, to achieve complex, high-level, long-term goals that are assigned to each agent individually. As the agents might not be capable of satisfying their respective goals by themselves, requests for other agents' collaborations are a part of the task descriptions. Particularly, we consider that the task specification takes a form of a linear temporal logic formula, which may contain requirements and constraints on the other agent's behavior. A traditional automata-based approach to multi-agent strategy synthesis from such specifications builds on centralized planning for the whole team and thus suffers from extreme computational demands. In this work, we aim at reducing the computational complexity by decomposing the strategy synthesis problem into short horizon planning problems that are solved iteratively, upon the run of the agents. We discuss the correctness of the solution and find assumptions, under which the proposed iterative algorithm leads to provable eventual satisfaction of the desired specifications.