Advanced quantum technologies, as well as fundamental tests of quantum physics, crucially require the interference of multiple single photons in linear-optics circuits. This interference can result in the bunching of photons into higher Fock states, leading to a complex bosonic behavior. These challenging tasks timely require to develop collective criteria to benchmark many independent initial resources. Here we determine whether independent imperfect single photons can ultimately bunch into the Fock state . We thereby introduce an experimental Fock-state bunching capability for single-photon sources, which uses phase-space interference for extreme bunching events as a quantifier. In contrast to autocorrelation functions, this operational approach takes into account not only residual multi-photon components but also a vacuum admixture and the dispersion of individual photon statistics. We apply this approach to high-purity single photons generated from an optical parametric oscillator and show that they can lead to a Fock-state capability of at least 14. Our work demonstrates a novel collective benchmark for single-photon sources and their use in subsequent stringent applications.