From 5.96 to 5.33 million years ago, disaster struck the Mediterranean Sea. A tectonic snag turned this...
...into something like this.
In this alternate scenario, the sea separating modern Europe from modern Africa isn't the Mediterranean, but one of our old friends, the Tethys.
As you can see, unlike the more shut-door Mediterranean, the Tethys has two openings--the Atlantic on one side and the Indian on another. Assume that the Tethys had its own salinity crisis in its geological history. With connections to both the Atlantic and the Indian, would the extent of evaporation and dehydration be as bad as back home? Better? Or worse?