  Results for $\beta$-functions and anomalous dimensions in general scalar
fermion theories are presented to three loops. Various constraints on the
individual coefficients for each diagram following from supersymmetry are
analysed. The results are used to discuss potential fixed points in the
$\varepsilon$-expansion for scalar fermion theories, with arbitrary numbers of
scalar fields, and where there are just two scalar couplings and one Yukawa
coupling. For different examples the fixed points follow a similar pattern as
the numbers of fermions is varied. For diagrams with subdivergences there are
extensive consistency constraints arising from the existence of a perturbative
$a$-function and these are analysed in detail. Further arbitrary scheme
variations which preserve the form of $\beta$ functions and anomalous
dimensions in terms of 1PI diagrams are also discussed. The existence of linear
and quadratic scheme invariants is demonstrated and the consistency condition
are shown to be expressible in terms of these invariants.
