  Asymptotically safe extensions of the Standard Model have been searched for
by adding vector-like fermions charged under the Standard Model gauge group and
having Yukawa-like interactions with new scalar fields. Here we study the
corresponding renormalization group beta functions to next and next-to-next to
leading order in the perturbative expansion, varying the number of extra
fermions and the representations they carry. We test the fixed points of the
beta functions against various criteria of perturbativity to single out those
that are potentially viable. We show that all the candidate ultraviolet fixed
points are unphysical for these models: either they are unstable under
radiative corrections, or they cannot be matched to the Standard Model at low
energies.
