Intel has the NUC Extremes which offer a full x16 slot in a fairly small footprint. The Core of the computer itself looks like a small GPU, and it plugs into a daughter board that acts as a coupler for its two x16 slots.
I think most people throw GPU's in them but I don't see a reason why you couldn't just fit it with a nice NIC
It has an external PCI-E 16x male port that goes into a small dock/riser where you can plug a graphics card for instance.
https://droix.co.uk/blogs/minisforum-b550-review/
A second review with a different conclusion: https://www.youtube.com/watch?v=ihcGnBjUAm4
Not so reasonably priced, so it maybe does not fit your criteria.