  The discrepancy between polarized and unpolarized measurements of the
proton's electromagnetic form factors is striking, and suggests that two-photon
exchange (TPE) may be playing a larger role in elastic electron-proton
scattering than is estimated in standard radiative corrections formulae. While
TPE is difficult to calculate in a model-independent way, it can be determined
experimentally from asymmetries between electron-proton and positron-proton
scattering. The possibility of a polarized positron beam at Jefferson Lab would
open the door to measurements of TPE using polarization observables. In these
proceedings, I examine the feasibility of measuring three such observables with
positron scattering. Polarization-transfer, specifically the
$\epsilon$-dependence for fixed $Q^2$, is an excellent test of TPE, and the
ability to compare electrons and positrons would lead to a drastic reduction of
systematics. However, such a measurement would be severely statistically
limited. Normal single-spin asymmetries (SSAs) probe the imaginary part of the
TPE amplitude and can be improved by simultaneous measurements with electron
and positron beams. Beam-normal SSAs are too small to be measured with the
proposed polarized positron beam, but target-normal SSAs could be feasibly
measured with unpolarized positrons in the spectrometer halls. This technique
should be included in the physics case for developing a positron source for
Jefferson Lab.
