I've encountered the following problem: when I connect 1 external usb hdd to my Pi, everything works fine. But when I connect second one with the same characteristics, both drives are not usable. I believe the problem is with drives' power consumption: each hard drive draws 1A from the USB port and as far as I understand raspberry pi3+ provides 1.2A to all the four usb-ports and this is maximum current available.
Is there a way to solve this problem (my current sata-USB cases DOES NOT have an external power supply, but if they had, would this help)? Ideally I'd like to connect four drives, but even two would be cool.