Computational studies of optimization problems on infrastructure networks may require more suitable instances than are available. We propose a method to obtain additional instances by extracting and joining connected parts of existing networks, reusing their topology and parameters. Many infrastructure networks are near-planar, so added connections should preserve this property. We measure near-planarity by skewness, the minimum number of edges whose removal makes a graph planar. We derive bounds on the additional skewness caused by joining and give sufficient conditions under which none is added, and propose the corresponding strategy. We evaluate our approach on 100 sets of network parts extracted from each of PGLib-OPF and SNDlib. Within time limits, we show that no skewness is added for about half of the resulting power transmission networks and all considered telecommunication networks. Our method gives smaller mean upper bounds on added skewness than baselines that select vertices randomly, in order of decreasing degree, or using a Kamada–Kawai layout. Extraction and composition may also make the resulting optimization instances infeasible. To reduce this risk, we solve a simpler, tractable variant of the intended optimization problem during generation and restart if it is infeasible. On the generated instances, we solve security-constrained optimal transmission switching and survivable network design problems in full, demonstrating that the instances vary in computational difficulty with runtimes ranging from seconds to hours. The method thus extends the available benchmark sets with instances that inherit source data, have known skewness bounds, and cover a range of computational difficulty.