Flexibly Stratified Comprehension is inconsistent. By Flexibly Stratified Comprehension, there is an s such that

∀x(xεs<-->∃y(∀t(tεy<-->tεx))∧y∉x). If sεs, then there is an S with the same members as s such that S∉s.

But if S∉s, then for all T with the same members as S, TεS. In particular SεS snd thus Sεs.

If s∉s, then for all S with the same members as s, Sεs. In particular sεs.

Flexibly Stratified Comprehension is inconsistent. By Flexibly Stratified Comprehension, there is an s such that

$$\forall x\:\bigl(x\in s\leftrightarrow\exists y\:\bigl(\forall t\:(t\in y\leftrightarrow t\in x)\land y\notin x\bigr)\bigr).$$ If $s\in s$, then there is an $S$ with the same members as $s$ such that $S\notin s$.

But if $S\notin s$, then for all $T$ with the same members as $S$, $T\in S$. In particular $S\in S$ and thus $S\in s$.

If $s\notin s$, then for all $S$ with the same members as $s$, $S\in s$. In particular $s\in s$.