I have shot hundreds and hundreds of rolls of Fuji Press 800 film, which I normally re-rate to EI400, as a matter of course. It can handle overexposure by an additional stop or two, it simply gets a bit grainier, and can consequently be slightly flatter-looking. That stuff is absolutely bulletproof, I love it. Works great in full sun, even at the beach.
Ken, It can also be shot at night, at EI 800, although, that's a bit of a stretch IMO. If the prints look "greyed-out and thin", that's an indication of underexposure.
Fuji Press 800 is about all we shoot here, it's also "cheap-cheap" from B&H in the 20-roll bulk-boxing. I have no idea why they sell so cheaply. Shhhhh!