  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 $1/N_F$. 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.
