In this chapter, we extend the scope of entropic fill, our innovative geometric measure for genuine multipartite entanglement (GME), to cover more general systems. To begin with, we explore the possibility of extending our measure to systems with more than four qubits. This involves deriving an analytical formula for the hypervolume of geometric simplices in spatial dimensions equal to or larger than four. Through this exploration, we embark on a geometric journey toward investigating multipartite entanglement. Subsequently, we extend our measure to encompass qudit systems, where each system party has more than two dimensions. This extension allows for the examination of multipartite entanglement across “multiple groups of parties.” Concluding this chapter, we will also discuss future research directions and potential applications of our geometric measure, particularly within the context of many-body quantum circuits and information scrambling.