It depends on the PC. If it's a mini ITX board with an unused 16 lane PCIe slot, you can put an adapter in there with 4 NVMe drives. Make sure the motherboard supports PCIe bifurcation though.
Another option is an M.2 to SATA adapter. They will connect 4 to 6 drives to an M.2 slot. Finding a place to mount those drives could be tricky though.
There are USB enclosures that provide more than 1 drive; what you're after is a 'usb attached das'/'usb direct attached storage'.
Caveat with these is not all of them are the same, and you'll want to validate the chipset they use works for your use case/OS or you can end up with a lovely pile of drives, all with corrupt data. (Cheap is not your friend here.)
Most likely the answer is "very little" or "not at all".
I have a SFF box that can support, max, 3 SATA drives (2.5"), because of lack of ports and little space. But it has the power to run 5. So I put in a PCI SATA controller, and wedged them in. Runs fine.