  We evaluate the two-photon exchange contribution to the $e N \to e
\Delta(1232) \to e \pi N$ process at large momentum transfer with the aim of a
precision study of the ratios of electric quadrupole (E2) and Coulomb
quadrupole (C2) to the magnetic dipole (M1) $\gamma^* N \Delta$ transitions. We
relate the two-photon exchange amplitude to the $N \to \Delta$ generalized
parton distributions and obtain a quantitative estimate of the two-photon
effects. The two-photon exchange corrections to the C2/M1 ratio depend strongly
on whether this quantity is obtained from an interference cross section or from
the Rosenbluth-type cross sections, in similarity with the elastic, $e N \to e
N$, process.
