Abstract: We analyze the implications for New Physics theories of an enhanced Higgs to di-photon rate. We show that models predicting a sizable enhancement have generically an electroweak vacuum that is not absolutely stable. In particular we discuss the only viable scenario, in the framework of the MSSM, that can predict sizable New Physics effects in the di-photon rate with all the other Higgs rates SM like: a scenario with light and highly mixed staus. We conclude with the phenomenology of the model and with the prospects of probing it at the LHC, through a multilepton signature.