Recent classification efforts encompassing crystalline symmetries have revealed rich possibilities for solid-state systems to support a tapestry of exotic topological states. However, finding materials that realize such states remains a daunting challenge. Here, we show how the interplay of topology, symmetry, and magnetism combined with doping and external electric and magnetic field controls can be used to drive the SrIn2As2 materials family into a variety of topological phases. Our first-principles calculations and symmetry analysis reveal that SrIn2As2 is a dual topological insulator with Z2=(1;000) and mirror Chern number CM=-1. Its isostructural and isovalent antiferromagnetic cousin EuIn2As2 is found to be an axion insulator with Z4=2. The broken time-reversal symmetry via Eu doping in Sr1-xEuxIn2As2 results in a higher-order or topological crystalline insulator state depending on the orientation of the magnetic easy axis. We also find that antiferromagnetic EuIn2P2 is a trivial insulator with Z4=0, and that it undergoes a magnetic-field-driven transition to an ideal Weyl fermion or nodal fermion state with Z4=1 with applied magnetic field. Our study identifies Sr1-xEuxIn2(As,P)2 as a tunable materials platform for investigating the physics and applications of Weyl and nodal fermions in the scaffolding of crystalline and axion insulator states.
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