This problem was already solved 10 years ago - crypto mining motherboards, which have a large number of PCIe slots, a CPU socket, one memory slot, and not much else.
> Asus made a crypto-mining motherboard that supports up to 20 GPUs
https://www.theverge.com/2018/5/30/17408610/asus-crypto-mini...
For LLMs you'll probably want a different setup, with some memory too, some m.2 storage.
In theory, it’s only sufficient for pipeline parallel due to limited lanes and interconnect bandwidth.
Generally, scalability on consumer GPUs falls off between 4-8 GPUs for most. Those running more GPUs are typically using a higher quantity of smaller GPUs for cost effectiveness.
M.2 is mostly just a different form factor for PCIe anyway.
Those only gave each GPU a single PCIe lane though, since crypto mining barely needed to move any data around. If your application doesn't fit that mould then you'll need a much, much more expensive platform.