Asymptotically Safe Standard Model Extensions?

We consider theories with a large number $N_F$ of charged fermions and compute the renormalisation group equations for the gauge, Yukawa and quartic couplings resummed at leading order in $1\mathrm{/}{N}_F$. We construct extensions of the Standard Model where SU(2) and/or SU(3) are asymptotically safe. When the same procedure is applied to the Abelian U(1) factor, we find that the Higgs quartic can not be made asymptotically safe and stay perturbative at the same time.