What happens when positronium atoms are created at a high density and are able to interact with each other? This is a question that may now be addressed experimentally with the advent of high-intensity low-energy positron pulses derived from a Surko trap. By creating bursts of positrons with spatiotemporal densities up to 10²⁰ cm⁻² s⁻¹ and implanting them into suitable materials, it is possible to observe “many positron” processes, such as Ps-Ps scattering and Ps₂ molecule formation. Here I shall describe various experiments we have conducted using high intensity and high density positron pulses, and outline our plans for future work.