  In rare-earth permanent magnets (REPM's), trade-off's between intrinsic
magnetic properties are often encountered. A recent example is SmFe$_{12}$
where excellent magnetic properties can be achieved at the sacrifice of bulk
structure stability. Bulk structure stability is sustained by the presence of
the third substitute element as is the case with SmFe$_{11}$Ti, where Ti
degrades magnetic properties. It is now in high demand to find out with which
chemical composition a good compromise in the trade-off between structure
stability and strong ferromagnetism is reached. We inspect the effects of
representative substitute elements, Zr, Ti, and Co in SmFe$_{12}$ by combining
ab initio data with experimental data from neutron diffraction. The trend in
the intrinsic properties with respect to the concentration of substitute
elements are monitored and a systematic way to search the best compromise is
constructed. A certain minimum amount of Ti is identified with respect to the
added amount of Co and Zr. It is found that Zr brings about a positive effect
on magnetization, in line with recent experimental developments, and we argue
that this can be understood as an effective doping of extra electrons.
