  The proton electric and magnetic form factors, $G_E$ and $G_M$, are
intrinsically connected to the spatial distribution of charge and magnetization
in the proton. For decades, Rosenbluth separation measurement, based on
measurements of the angular dependence of elastic electron-proton scattering,
were used to separate $G_E$ and $G_M$. More recently, polarized electron
scattering measurements were used to improve the precision of the separation
but showed significant disagreement with Rosenbluth measurements. The
discrepancy was confirmed using a new `Super-Rosenbluth' technique to improve
the precision of the Rosenbluth extraction.
  This large and unexpected discrepancy raised significant questions about our
understanding of the proton, and became a high-priority issue for the field.
Since then, a string of theoretical and experimental studies attempting to
understand the discrepancy have led to the conclusion that two-photon exchange
(TPE) corrections are most likely responsible for the discrepancy. TPE can be
measured directly by comparing positron-proton (e$^+$p) and electron-proton
(e$^-$p) scattering, but these measurements are extremely challenging. To date,
TPE contributions have been directly observed only at lower $Q^2$ values, below
the region where the Rosenbluth and polarization measurements strongly
disagree.
  In this work, we show that there are significant benefits to combining the
Super-Rosenbluth technique with positron beam measurements. In addition to
providing improved precision and a greater kinematic reach, the use of the
Super-Rosenbluth technique provides a comparison of e$^+$ and e$^-$ scattering
that is insensitive to some of the key systematic uncertainties associated with
direct comparisons of e$^+$p to e$^-$p scattering.
