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 $$2.12\times 10^{35}$$
2.12
×
10
35
cm$$^{-2}\cdot $$
-
2
·
s$$^{-1}$$
-
1
($$\approx 200$$
≈
200
times the luminosity achieved by OLYMPUS). The proposed two-photon exchange experiment (TPEX) entails a commissioning run at a beam energy of 2 GeV, followed by measurements at 3 GeV, thereby providing new data up to $$Q^2=4.6$$
Q
2
=
4.6
(GeV/c)$$^2$$
2
(twice the range of current measurements). We present and discuss the proposed experimental setup, run plan, and expectations.