The project will begin with using a simpler extension of the Standard Model, the Two Higgs doublet model (2HDM) with the aim of replicating phenomenological results, using the code BSMPT, regarding the size of coupling strengths in interactions relevant to di-Higgs production at the LHC and the HL-LHC. Then we will move on to consider a more sophisticated SM extension, the Next-2-Higgs-Doublet Model (N2HDM), to calculate the same coupling constants with the hope to draw conclusions about the shape of the scalar Higgs potential and the nature of the electroweak phase transition (EWPT) in the early universe. For the latter, we specifically attempt to discern between the cases of a first order EWPT and a second order EWPT which is predicted by the Standard Model.