You can use an external SSD – but the available interfaces will bottleneck transfers to and from the SSD, so you will not see blazing speed. Much of the time, you might not see much more speed than you would get if you were using a mechanical hard drive. When I was using a FireWire 800 SSD, the only time I saw huge speedups was when I was running Windows 10, under Parallels Desktop, within 8 GB of RAM. (Then, things went from painfully slow to merely slow, thanks to the improvement in random access times.)
FireWire 800 is the fastest external drive interface on your Mac, but as far as I know, there is only one source left for FireWire drives and enclosures.
Other World Computing – FireWire Drives
They appear to be out of the silent bus-powered notebook ones – perhaps permanently.