In this paper we investigate supervisor synthesis for a multi-agent system, which consists of an indefinite number of agents, all instantiated from a given agent template via corresponding language isomorphisms. We call such a system a multi-agent system with similar actions, as their individual alphabets are isomorphic to each other. Each agent shares a common global alphabet with other agents, but their private alphabets are disjoint. All local requirements are also instantiated from a given requirement template. We formulate a control protocol synthesis problem, which assumes that each private alphabet is only observable to the corresponding agent, but the global alphabet is accessible by all agents. Our goal is to compute a control protocol (i.e., a supervisor template) whose instantiations associated with individual agents ensure a controllable, nonblocking and requirement-satisfying behavior of the system, regardless of the total number of constituent agents. A solution to this problem will make the desirable plug-and-play control strategy feasible. We show that the existence of a solution is decidable, and a solution is computable when the answer to the decision problem is positive. To overcome the synthesis complexity, a polynomial-time heuristic algorithm is provided. (C) 2017 Elsevier Ltd. All rights reserved.