Take a look at the IODD ST400.
It's a hardware solution to your problem: you put multiple isos on an ssd, plug your ssd into the ST400, then plug the ST400 into the computer you want to live boot from (through USB).
From the ST400 you can quickly swap the active ISO, and it acts like a virtual DVD drive to the target computer, and you're basically ejecting and inserting a new DVD every time you do so.
You can also mount it for RW operations (ie. for inserting new ISOs without having to remove the SSD), for which it acts like a regular usb disk - but I recommend using it usually in RO mode to avoid data corruption.
It's not that user friendly, but once you get used to it, it's a perfect multiboot tool to have in your belt.