The Electron-Ion Collider is under construction at BNL. It will have high-energy high-intensity polarized beams of electrons and hadrons. These beams will allow a high accuracy investigation of nucleon structure in the low- to very-low-x DIS regime. At the same time, similar to the realization at HERA, these beams could be used with an internal target for a very productive investigation of medium- to high-x nucleon structure. Due to a novel regime of electron beam operation and its high polarization and intensity, the Figure-of-Merit of an internal target experiment at EIC will be 500+ times higher than was obtained by HERMES.