Rank-one Update to a Rank Revealing QR (RRQR) Factorization?

Suppose we are given an RRQR factorization for some matrix $A \in \mathbb{R}^{m \times n}$, $A\Pi = QR$ where $m > n$.

Is there a cheap way to update $A' = A + uv^{\top}$ given this factorization?

I am aware of how to update the QR factorization given a rank-one update, but I am unsure how to update $\Pi$ as well to guarantee the rank-revealing aspect.