We show the reinterpretation of existing searches for exotic decays of the Standard Model (SM)-like Higgs, $H \to aa (hh)$, in various final states, in the framework of the 2-Higgs Doublet Model (2HDM) Type-I. We then explore a new search for such light Higgses, $a$ and $h$, at the Large Hadron Collider (LHC) Run 3 for an integrated luminosity of 300 $\text{fb}^{-1}$. After performing a scan over the model parameters, we found that the inverted scenario of Type-I offers a new promising signal in the form of the following cascade decays: $H \to Z^{*}a \to Z^{*}Z^{*}h \to b\overline{b} \mu^- \mu^+ jj$. We investigate then its significance through a full Monte Carlo (MC) simulation down to the detector level.