  Given a closed subgroup $G\subset U_N^+$ which is homogeneous, in the sense
that we have $S_N\subset G\subset U_N^+$, the corresponding Tannakian category
$C$ must satisfy $span(\mathcal{NC}_2)\subset C\subset span(P)$. Based on this
observation, we construct a certain integer $p\in\mathbb N\cup\{\infty\}$, that
we call "easiness level" of $G$. The value $p=1$ corresponds to the case where
$G$ is easy, and we explore here, with some theory and examples, the case
$p>1$. As a main application, we show that $S_N\subset S_N^+$ and other
liberation inclusions, known to be maximal in the easy setting, remain maximal
at the easiness level $p=2$ as well.
