This is all but impossible to do without some major compromises, even when going the custom built route. NUCs are consumer machines so Intel is going to go for the base use case. Never going to happen.
AFAIK, there aren’t any suitable mITX custom cases that support this. 3 slots would require mDTX support at a minimum, assuming that the 10 GbE NIC is going to run off a PCIe riser from a M.2 x4, and a slot configuration that supports a dual x8 riser, assuming the main PCIe slot can be bifurcated. There are a few mDTX mobos but they are all the ASUS Impact line which are hideously expensive.
Best bet would be a mATX mobo in a case as small as you can get, possibly a Sliger (which is also expensive).