How much range a multi-engine plane could gain by shutting down one engine in flight?

Or would the speed be reduced so much that whatever one gains in lower fuel burn, one loses due to increased flight time?

And are there any situations where this might be practiced to keep the plane in the air for longer? I was wondering if military surveillance planes for instance ever do this for increased endurance, once on station.

I’ve been wondering this for years, so thought to ask from people who really know. Thank you in advance!