When expanding an existing public transport system a common practice consists of defining a set of candidate new lines and from them, choose those that will revert into a greater increase of the system’s performance while keeping at a moderate level the associated amount of economical costs. In this work, a mathematical programming model for the selection of candidate lines in extensions of the public transport system is proposed based on the linearization of the model presented by Codina et al. (2013) and its application to situations of medium congestion. The model assumes that the pool of candidate lines is an input externally determined by technical criteria and it is focused in the compatibility constraints that the final set of selected lines must verify. These constraints include the overall throughput capacity of the stops/stations of the model, the availability of space for users to wait at stations, the resulting line capacities for passenger flows at line segments and the waiting times of passengers at stops. Solution procedures are based on the Cutting Plane’s algorithm and several small to medium size instances are successfully solved in the computational tests.