  The Mu2e experiment at Fermilab is being designed to study the coherent
neutrino-less conversion of a negative muon into an electron in the field of a
nucleus. This process has an extremely low probability in the Standard Model
and its observation would provide unambiguous evidence for BSM physics. The
Mu2e design aims to reach a single-event-sensitivity of about $2.5 \times
10^{17}$ and will probe effective new physics mass scales in the 103-104 TeV
range, well beyond the reach of the LHC. This work examines the maximum beam
power that can be tolerated for beam energies in the 0.5-8 GeV range exploring
variations in the geometry in the region of the production target using the
MARS15 code. This has implications for how the sensitivity might be further
improved with a second generation experiment using an upgraded proton beam from
the PIP-II project, which will be capable of providing MW beams to Fermilab
experiments later in the next decade.
