Intel Xeon motherboards can have (currently) up to 8 sockets. Just search for “8 socket motherboard” and you will find them.
A quick look did not find AMD motherboards that could hold 8 sockets.
I have not heard of any 16-sockets systems.
It is not entirely clear under what conditions you want such a thing. One use case would be applications that need a great number of threads running in a coherent shared memory address space. This sort of thing might be useful, for example, in DNA sequencing with very large RAM, but not too much bandwidth per thread. They might also be useful as in-memory database machines, but that’s not my area.
8-socket systems will cost more per socket than 4 socket systems, which cost more per socket than 2-socket systems, and so forth. The reason for this is that you need rather expensive motherboards to get the intersocket connections routed correctly. If you don’t need a very large shared memory, you can get more computing per dollar with smaller servers and a fast network.
Back at SiCortex our boards had 27 processor sockets, each with 2 DIMM sockets, but that was an unusual system and not x86 compatible :)