It's definitely possible. Has someone built exactly that? I don't know; there are hundreds of variants of single-board computers, and I'm only familiar with a few. It's not something that you'd build by buying a couple of parts and soldering them to a breadboard.
As for attaching memory, GPIO probably gives you a transfer rate on the order of a few MB/s. There are various things like SPI-connected SRAM chips, but those don't provide a lot of memory (think KB, not GB).
DDRAM requires too much speed to do something through the GPIO or USB... What you could do is use the Tinkerboard S, boot off of a microSD card and use the integrated eMMC storage as a big 16gb swap partition... or just partition the eMMC into an 8gb boot and 8gb swap to give you 10gb usable.