Motivated by the problem of market power in electricity markets, we introduced in previous works a mechanism for simplified markets of two agents with linear cost. In standard procurement auctions, the market power resulting from the quadratic transmission losses allows the producers to bid above their true values, which are their production cost. The mechanism proposed in the previous paper optimally reduces the producers' margin to the society's benefit. In this paper, we extend those results to a more general market made of a finite number of agents with piecewise linear cost functions, which makes the problem more difficult, but simultaneously more realistic. We show that the methodology works for a large class of externalities. We also provide an algorithm to solve the principal allocation problem. Our contribution provides a benchmark to assess the sub-optimality of the mechanisms used in practice.