The Muon g − 2 Experiment now running at Fermilab aims to resolve the current 3.7σ experiment-theory discrepancy in the anomalous mag- netic moment of the muon, aμ = (g − 2)/2. Among the possible sources of new physics that could account for a non-zero value for aμ are CPT or Lorentz Invariance violations. Previous muon g − 2 experiments have set the majority of the most stringent limits on Standard-Model Extension CPT and Lorentz violation in the muon sector. These limits are consistent with calculations of the level of Standard-Model Extension effects required to account for the current aμ discrepancy. The status and prospects of the Fermilab Muon g − 2 Experiment searches for CPT/Lorentz violation will be discussed, and possibilities for additional new physics investigations at Muon g − 2 using similar techniques will also be presented.