If $X\to Y$ is a quasi-finite map of finite presentation between qcqs schemes and $U\subseteq X$ is open such that $U\to Y$ is flat, then we have the following two results:
Raynaud-Gruson’s platification: there is a $U$-admissible blow-up $Y’\to Y$ such that the strict transform of $X$ is flat over $Y’$
Zariski's main theorem: $X\to Y$ factors as an open immersion $X\to Y$ and a finite morphism $Y’\to Y$
My question is the following: is it possible to combine those two results and say something like “a quasi-finite map can be refined by a flat map and a finite map”, i.e. make the admissible blow-up in 1. finite?
