Software-defined network (SDN) is a network that the centralized SDN controller stores flow entries in the flow table of each SDN switch and controls packet flows as instructed by the stored flow entries. When a multicast service is provided in an SDN, the SDN controller stores a multicast entry dedicated for a multicast group in each SDN switch. It is necessary to suppress the number of flow entries required to set up a multicast tree due to the limited capacity of the flow table. In a conventional research, a multicast routing model that suppresses the number of multicast entries in one multicast request by replacing a part of them with unicast entries has been devised. However, since this conventional model individually determines a multicast tree route for each request, unicast entries configured for the same receiver are distributed in various SDN switches when multiple multicast services are requested. As a result, there is still the possibility of improving the reduction of the number of flow entries. In this paper, we propose a multicast routing model for multiple multicast requests that minimizes the number of flow entries. This proposed model determines multiple multicast tree routes simultaneously so that a unicast entry configured for the same receiver and stored in the same SDN switch is shared by multicast trees. We formulate the proposed model as an Integer Linear Programming (ILP) problem. Numerical results show that the proposed model reduces the required number of flow entries compared to the conventional model.