It depends on what you mean by "fully open" (i.e. you want the mask set and design files too...?), but if you're just looking for a PC-on-a-chip, there's this:

http://www.dmp.com.tw/tech/vortex86dx/

The site looks old but according to this, it's still in production:

https://www.allaboutcircuits.com/news/are-designers-still-us...

Actually that's pretty much exactly the kind of thing I was looking for. Thanks.

Intel could have put a low-end GPU on a version of Quark.