*

Aided by a refined understanding of topological band structures with crystalline symmetries that has emerged recently, many electronic phases have been identified and a plethora of materials have been predicted to host novel properties and functionalities. Here we describe a paradigmatic semimetal that simultaneously incorporates multiple, and sometimes conflicting topology which guarantees gaplessness and leads to an exceptionally rich family of descendent phases on lowering symmetry. We predict that this multicritical phase is realized in EuTl₂. Starting from the parent semimetallic state, which already separates two topological insulating regimes, the interplay of inherent magnetism and strain allows for an exceptionally rich phase diagram of topological descendant states.