In this paper, we propose a virtual network function placement and routing model for multicast service chaining based on merging multiple service paths (MSC-M). The multicast service chaining (MSC) provides a multicast path, which connects a source node and multiple destination nodes, and virtual network functions (VNFs) are placed on the path so that users on the destination nodes receive their desired services. The conventional MSC model configures multicast paths for services, each of which has the same source data and the same set of VNFs in a predefined order. In the MSC-M model, if paths of different services carry the same data on the same link, these paths are allowed to be merged into one path at that link, which improves the utilization of network resources. The MSC-M model determines the placement of VNFs and the route of paths so that the total cost associated with VNF placement and link usage is minimized. The MSC-M model is formulated as an integer linear programming (ILP) problem. In the ILP problem, data flows whose source data is the same and which already passed the same subset of VNFs belong to the same group. A part of paths of different services which carry data flows belonging to the same group are allowed to be merged into one path. Numerical results show that the MSC-M model reduces the total cost by 28.7% at a maximum compared to the conventional MSC model.