Abstract We investigate the fixed point properties for sublogics of the interpretability logic $\textbf {IL}$. In our previous work, it was proved that a sublogic $\textbf {IL}^{-}(\textbf {J 2}_+, \textbf {J 5})$ has the fixed point property (FPP) and that a sublogic $\textbf {IL}^{-}(\textbf {J 4}, \textbf {J 5})$ has a newly introduced weaker property $\ell $FPP. In this paper, we provide countably many sublogics of $\textbf {IL}^{-}(\textbf {J 2}_{+}, \textbf {J 5})$ (resp. $\textbf {IL}^{-}(\textbf {J 4}, \textbf {J 5})$) having FPP (resp. $\ell $FPP).