  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 beyond the standard
model 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 will examine
the maximum beam power that can be tolerated for beam energies in the 0.5-8 GeV
range. 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.
