The factorization of exclusive processes can give access to generalized transverse momentum-dependent distributions (GTMDs). We consider here the case of the differential cross-section for the exclusive process $\pi N\rightarrow N' \gamma^* \gamma^*\rightarrow p (\ell^+\ell^-)(\ell^+\ell^-)$. We provide a factorization theorem for this process studying the gauge links that are involved and providing an expression of the cross-section factorized in terms of two GTMDs and two light-cone wave functions. Furthermore, we show that the soft radiation has a structure very similar to the one found in single parton scattering. Finally, the cancellation of rapidity divergences is also studied.