In this talk, I will define the d-th mode transition algebras, introduced in recent joint work with Chiara Damiolini, myself, and Danny Krashen. This series of associative algebras reflect properties of algebraic structures on moduli of stable pointed curves and representations of the vertex algebras from which they are derived. I will discuss new work with Danny and Chiara, where we show that under natural assumptions, the categories of unital modules over the d-th mode transition algebras and Zhu's associative algebra are equivalent. These Morita equivalences allow one to obtain explicit expressions for higher level Zhu algebras as products of matrices, generalizing the result for vertex algebras defined by 1 dimensional Heisenberg Lie algebras from our previous work. This theory applies for instance, to certain VOAs with commutative and connected Zhu algebras, and to rational vertex algebras.