  We study four-dimensional gauge theories coupled to fermions in the
fundamental and meson-like scalars. All requisite beta functions are provided
for general gauge group and fermion representation. In the regime where
asymptotic freedom is absent, we determine all interacting fixed points using
perturbation theory up to three loop in the gauge and two loop in the Yukawa
and quartic couplings. We find that the conformal window of ultraviolet fixed
points is narrowed-down by finite-$N$ corrections beyond the Veneziano limit.
We also find a new infrared fixed point whose main features such as scaling
exponents, UV-IR connecting trajectories, and phase diagram are provided. Both
fixed points collide upon varying the number of fermion flavours $N_{\rm f}$,
and conformality is lost through a saddle-node bifurcation. We further revisit
the prospect for ultraviolet fixed points in the large $N_{\rm f}$ limit where
matter field fluctuations dominate. Unlike at weak coupling, we do not find
clear evidence for new scaling solutions even in the presence of scalar and
Yukawa couplings.
