ROTTERDAM, the Netherlands — Sjarel Ex stood in the basement of the Boijmans van Beuningen Museum, ankle-deep in rising waters, facing a Sophie’s choice.

Rotterdam’s fire chief had told him that the paintings collection would be destroyed within 30 minutes unless Mr. Ex, a co-director of the museum, gave permission to sandbag the library, sacrificing the books.

In the end, the art was saved and only a couple hundred volumes lost. But the 2013 event catalyzed Mr. Ex’s campaign to move the museum’s collection. “From that moment on, we were not so very polite about the need to have a new storage facility,” he said.

He fought for this as part of a plan to close the 1935 museum for renovations, which were already under discussion.