Gauge boson masses dominantly generated by Higgs-triplet contributions?

We discuss a model in which the Standard Model (SM) Higgs sector has been extended by additional real and complex triplets. The $\rho\approx 1$ constraint is satisfied by restricting the potential to have an enlarged $\hisym $ global symmetry. This is fine tuning, which leads to a decreased predictability in next-to-leading order. In this model, however, the triplet vacuum expectation values may give the dominating contribution to the gauge boson masses. Using a renormalization group argument we constrain this region of the parameter space. Another interesting feature of this model is that one of the neutral scalars doesn't couple to the fermion sector at tree level and therefore could have a relatively large branching ratio to $2\gamma $'s. It is coupled, however, to the $Z$-boson and therefore it could be produced at LEP via the standard $e^+e^-\rightarrow Z\phi$ mechanism with rates comparable to the ones of the Standard Model.