  We describe an integrated modelling approach to accelerate the search for
novel, single-phase, multicomponent materials with high magnetocrystalline
anisotropy (MCA). For a given system we predict the nature of atomic ordering,
its dependence on the magnetic state, and then proceed to describe the
consequent MCA. Crucially, within our modelling framework, the same ab initio
description of the material's electronic structure determines both aspects. We
demonstrate this holistic method by studying the effects of alloying additions
in FeNi, examining systems with the general stoichiometry Fe$_4$Ni$_3X$,
including $X = $ Pt, Pd, Al, and Co. The atomic ordering behaviour predicted on
adding these elements, fundamental for determining a material's MCA, is rich
and varied. Equiatomic FeNi has been reported to require ferromagnetic order to
establish the tetragonal $\mathrm{L}1_0$ order suited for significant MCA. Our
results show that when alloying additions are included in this material,
annealing in an applied magnetic field and/or below a material's Curie
temperature may also promote tetragonal order, along with an appreciable effect
on the predicted MCA.
