We propose a scheme for Cloud-of-Things and Edge Computing (CoTEC) traffic management in multi-domain networks. To direct the traffic flow through the service nodes, we assign a critical egress point for each traffic flow in the CoTEC network using multiple egress routers to optimize the traffic flow; this is known as Egress-Topology (ET). Therefore, the proposed ET incorporates traditional multi-topology routing in the CoTEC network to address the inconsistencies between service overlay routing and the border gateway protocol policies. Furthermore, the proposed ET introduces a number of programmable nodes that can be configured to ease the ongoing traffic on the network and re-align services among the other nodes in multi-domain networks. The results show that our algorithm has a lower execution time and better quality of service than that obtained without using our algorithm, thus allowing us to satisfy the flexibility and efficiency demands of multi-domain networks.