are two important requirements from current experimental data. First of all, the data indicate that the electroweak rho parameter ($\rho$) is very close to unity. Second, flavor of quarks and charged leptons is (approximately) conserved in the neutral current. In the SM, these two conditions are satisfied respectively by the custodial symmetry which ensures $\rho=1$ at the tree level, and by the Glashow-Iliopoulos-Maiani (GIM) mechanism which prohibits the tree-level flavor changing neutral current (FCNC). Needless to say that these experimental requirements must be respected in extended Higgs models which would appear in the low energy effective theory of a more fundamental theory beyond the SM.

Extension of the SM Higgs sector can be considered by including additional scalar isospin singlets, doublets and higher multiplets. It is known that additional singlets and doublets keep $\rho=1$ at the tree level [@Gildener:1976ih]. Radiative corrections can slightly deviate the rho parameter from unity, corresponding to explicit violation of the custodial symmetry in the dynamics in the loop. On the other hand, extension with higher multiplets such as triplets is usually problematic, predicting the rho parameter to be explicitly different from unity already at the tree level [@Gunion:1992hs]. One way to avoid this problem is 