  The past decades have witnessed a transformation in characterizing condensed
matter systems with topology. 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. A key underlying
question, also with respect to future application, is to what extent the
related physical features can be manipulated, especially in the context of
magnetic order. 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.
