The relatively unexplored family of pnictide-based antiperovskites has been shown to harbor prospects for topological phases. Using the example of Ca3BiP, we demonstrate a cascade of phases as the initial cubic symmetry is broken successively. Initially a small gap Z2 topological insulator, spin-orbit coupling leads to band reordering resulting in a topological semimetal phase. Compressive uniaxial (001) strain leads back to a small gap Z2 topological insulator, with the expected gapless boundary modes. Tensile (001) strain leaves the system with a pair of Dirac points along (0,0,±k•) pinning the Fermi level, producing an unusual double meniscus of connected Fermi arcs on the (100) and (010) surfaces. Finally, breaking time-reversal symmetry by an applied Zeeman field produces a new phase with a pair of multi-Weyl nodes (massive or massless depending on direction, conventionally called semi-Dirac in two dimensional systems) simultaneous with a sister pair of Dirac modes along each ±kz axis, combining to pin the Fermi level in the close vicinity of these varied single-particle excitations.