There are quiet usable external PCIx cases for Thunderbolt 1.2 and will be even better for 1.3 but can you see Thunderbolt at your G20AJ ?
(TB 1.3: Razer "Core", Asus "ROG XG2")
Anyway those cases are not cheap at all, f.e. the Sonnet Echo Express III-D case that can take up a full length full width card ist about 750€ at least, if you´re lucky.
Besides this would kill the "super-compact" concept more or less, I would prefer a regular PC then which is just a little bit bigger but offer a ton of comfort and features in absolutely any way which the G20 does not.