Phenomenology of models with more than two Higgs doublets
  We study the most general Multi-Higgs-Doublet Model (MHDM) with Natural Flavor Conservation (NFC). The couplings of a charged scalar $H_i^{\pm}$ to up quarks, down quarks and charged leptons depend on three new complex parameters, $X_i$, $Y_i$ and $Z_i$, respectively. We prove relations among these parameters. We carry out a comprehensive analysis of phenomenological constraints on the couplings of the lightest charged scalar: $X$, $Y$ and $Z$. We find that the general MHDM may differ significantly from its minimal version, the Two-Higgs-Doublet Model (2HDM). 
Yuval Grossman