  We propose a new measurement of the ratio of positron-proton to
electron-proton elastic scattering at DESY. The purpose is to determine the
contributions beyond single-photon exchange, which are essential for the
Quantum Electrodynamic (QED) description of the most fundamental process in
hadronic physics. By utilizing a 20 cm long liquid hydrogen target in
conjunction with the extracted beam from the DESY synchrotron, we can achieve
an average luminosity of $2.12\times10^{35}$
cm$^{-2}\cdot$s$^{-1}\cdot$sr$^{-1}$ ($\approx200$ times the luminosity
achieved by OLYMPUS). The proposed TPEX experiment entails a commissioning run
at 2 GeV, followed by measurements at 3 GeV, thereby providing new data up to
$Q^2=4.6$ (GeV/$c$)$^2$ (twice the range of current measurements). We present
and discuss the proposed experimental setup, run plan, and expectations.
