This question is a following up [this][1].

Is it consistent for *ALL* infinite stages $V_{\alpha >  \omega}$ of the cumulative hierarchy of $\sf ZF$, to violate the weak partition principle? That is, each $V_{\alpha >  \omega}$ can be parititioned into strictly more many compartments than its elements.


  [1]: https://mathoverflow.net/questions/424415/can-a-stage-of-the-cumulative-hierarchy-violate-the-partition-principle