The Two Higgs Doublet Model and the Multiple Point Principle
  According to the multiple point principle, Nature adjusts coupling parameters so that many vacuum states exist and each has approximately zero vacuum energy density. We apply this principle to the general two-Higgs doublet extension of the Standard Model, by requiring the existence of a large set of degenerate vacua at an energy scale much higher than the presently realized electroweak scale vacuum. It turns out that two scenarios are allowed. In the first scenario, a CP conserving Higgs potential and the absence of flavour changing neutral currents are obtained without fine-tuning. In the second scenario, the photon becomes massive in the high scale vacua. We briefly discuss the resulting phenomenology. 
C.D. Froggatt, L.V. Laperashvili, R.B. Nevzorov, H.B. Nielsen, M. Sher