The CMS group has reported an anomaly in the production of particles at ~95 GeV above expected background at the LHC in the ditau and diphoton channels. Taken with a similar anomaly detected in the diphoton channel by ATLAS and an older result from the LEP showing an anomaly in $b\bar{b}$ production, this indicates the prospect of a new particle with $m=95$ GeV. As a possible explanation for these anomalies, we consider a pair of Simplified Models that add an additional Higgs doublet to the Standard Model--- realizing the well-known Two-Higgs Doublet Model (2HDM)---as well as an additional scalar or pseudoscalar gauge singlet. We investigate the possibility that the lightest scalar or pseudoscalar state in these models could have a mass of 95 GeV, generating the observed excesses. We apply relevant bounds from flavour physics (primarily from rare decays of B-mesons), collider physics (resonance and missing transverse energy searches), and Higgs physics to determine if these constraints can be satisfied while still generating the observed excesses. We find that both models could generate the anomalies seen at the LHC, but neither can effectively reproduce the $b\bar{b}$ anomaly at the LEP.