My son ran out of room on his PS4. I already have a 4 (or 8? I can’t remember) TB external drive on my PS4.
It just so happens that my son’s tv is on the opposite side of the wall where MY tv is. So it would be real easy (and cheap) to just poke a cable through the wall and hook his PS4 to my external drive.
At the same time? Certainly not.
One at a time? Conceivably, but you might end up with things like overwriting each others’ saves.
Do they use a proprietary file system or partition type? Because you might could do what Chronos suggests with a switch and two different partitions, which would avoid the overwriting saves issue. You’d still need to be sure the other person wasn’t using it, though.
But, honestly, unless you’re really scraping for cash, it would probably be easier to get another hard drive. You may be able to get a better deal with an internal drive and a SATA to USB 3 converter rather than an external–especially if you’re willing to use refurbished–just make sure that a refurbished drive has a good warranty–I wouldn’t go less than 3 years, myself.
Forget that–just upgrade the PS4’s internal drive. It’s made to have its hard drive easily replaceable by the end-user. There are published instructions for it on Sony’s website. I replaced my PS4 stock drive with a 2tb drive. All you need is a Phillips head screwdriver. It’s literally a matter of sliding off the case and removing 5 screws. If you want to have as much storage as possible, you can keep the stock drve and put it in a $10 enclosure with a SATA to USB connector on it. (Which is what I did, but I haven’t even used any of the space on the stock drive yet.)
And the PS4 supports FAT32 and exFAT, but I don’t think it’s possible to use multiple partitions with it.