When one charged lepton gets mass through the SM Higgs boson and two others through a different $SU(2)_L$ doublet, what are the constraints on VEVs?

Question

If one charged lepton receives its mass through the SM Higgs boson ($H$), while two others through a different $SU(2)_L$ doublet ($\phi_2$ and $\phi_3$). What are the constraints on this new scalar doublet, and in particular, on its vacuum expectation value. Does it follows $<v_1>^2 + <v_2>^2 +<v_3>^2=(246GeV)^2$. $v_1$, $v_2$ and $v_3$ are the VEVs of $H$, $\phi_2$ and $\phi_3$ respectively.