Hyperalgebras and BCI algebras extend classical algebraic structures, and these specific structures offer tools and frameworks for studying various operations and logic in algebra. Many authors continued their research in hyperstructures to explore different logical algebras. SuperHyper Algebra is one of the significant advancements in algebra which has been developed recently. In this article, we propose a generalized concept, namely, SuperHyper BCI-Algebra, and investigate some of its properties. We also define SuperHyper Subalgebra, and some of its characteristics are examined. Finally, we extend our vision to Neutrosophic SuperHyper BCI-Algebra.