In the design of wire-based networks, the implementation of infrastructure is a major cost component. One way to obtain cost savings is to coordinate trenching activities of different network operators, e.g., telecommunication providers may join forces with local communities when digging roads or pavements. In this work, the Multi-Commodity Cable Trench Problem (MC-CTP) is introduced that aims at detecting cost minimizing network structures including the option to reduce trenching costs by a joint realization for different cable types. A mixed-integer linear programming model is proposed and strengthened through the development of valid inequalities. Moreover, complexity and solution properties, like the existence of rings are discussed. The numerical study includes two parts. First, the effect of the valid inequalities on the LP-relaxation is studied experimentally. Second, the impact of the trenching cost reduction on the degree of joint activities and on total costs is investigated.