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The Standard Model of Particle Physics is a very accurate description of nature. It is however incomplete, unable to explain phenomena such as the baryon asymmetry problem, the strong CP problem, and the nature of dark matter. In this thesis, I investigate two Simplified Models that extend the Standard Model and may be able to resolve some of these issues: the two Higgs doublet model (2HDM) with an additional singlet scalar (s) or pseudo-scalar (a). Assuming the Weakly Interacting Massive Particles (WIMP) model of Dark Matter, the 2HDM+a/s possess potential interaction portals between Standard Model and dark sector particles. The 2HDM+a/s also have the capability to explain the 95 GeV anomaly: the CMS and ATLAS groups have reported excesses in the production of tau lepton and photon pairs at the LHC at an invariant mass ~95 GeV, and an older result from the LEP reports a similar excess in the production of b-quark pairs. I investigate the possibility of all three anomalies being caused by a single BSM particle in the 2HDM+a/s. Along with fits to the anomalies and discussion of the dark matter phenomenology of the models, I apply constraints from flavour physics, precision electroweak tests, and collider physics to determine if the 2HDM+a/s remain as viable extensions of the Standard Model. I also discuss my ongoing work in implementing the 2HDM+a in the global model-analysis program GAMBIT.