Neutrosophic Sets are conceptual frameworks designed to address uncertainty. A Neutrosophic TwoFold Algebra is a hybrid algebraic structure defined over a neutrosophic set, combining classical algebraic operations with neutrosophic components. Concepts such as Hyperalgebra and Superhyperalgebra extend classical Algebra using Power Sets and n-th powersets. Additionally, structures such as NeutroAlgebra and AntiAlgebra have been defined in recent years. This paper explores several related concepts, including TwoFold SuperHyperAlgebra and Anti SuperHyperAlgebra.