The presence of galactic sources displaying a power-law dependence in their gamma-ray fluxes has been recently reported by gamma-ray observatories such as LHAASO and HAWC. This exciting discovery, with a few sources showing no cutoff in their flux, has the potential to enable measurements of photon fluxes at energies even higher than 10¹⁵ eV. To measure the tails of the energy spectra of these sources, we investigate the capabilities of a new dense array of water-Cherenkov detectors, the Project for Extreme PeVatron Sources (PEPS). To distinguish primary photons from the overwhelming cosmic-rays background, we investigate the performance of a detector that optically divides the water volume to separate the muonic component of air showers from the electromagnetic one. The expected sensitivity of these layered surface detectors, covering a 2 km 2 area at the site of the Pierre Auger Observatory, is presented. With the potential to make groundbreaking discoveries, such an array might represent a promising area of research in gamma-ray astronomy.