In this research immersion lab, we explore the expressiveness of Hyper$^2$LTL, which is a temporal logic designed to specify second-order hyperproperties. It extends HyperLTL by allowing quantification over sets of traces, which greatly enhances its expressive power and enables the expression of more complex properties such as common knowledge and asynchronous hyperproperties. Due to the novelty of the logic, limited research has been conducted to explore its expressiveness.  We investigate the expressive power of Hyper$^2$LTL and its relationship to well-known classes of formal languages.