Update (May 12th, 1:45am): Okay so the post has been deleted, which was originally from Chris Bencivenga, Support Manager at EVGA. A screenshot of it is attached below. Note that Jacob Freeman later posted that "More info about SLI support will be coming soon, please stay tuned." I guess this means take the news with a grain of salt until an official word can be released.
Original Post Below
According to EVGA, NVIDIA will not support three- and four-way SLI on the GeForce GTX 1080. They state that, even if you use the old, multi-way connectors, it will still be limited to two-way. The new SLI connector (called SLI HB) will provide better performance “than 2-way SLI did in the past on previous series”. This suggests that the old SLI connectors can be used with the GTX 1080, although with less performance and only for two cards.
This is the only hard information that we have on this change, but I will elaborate a bit based on what I know about graphics APIs. Basically, SLI (and CrossFire) are simplifications of the multi-GPU load-balancing problems such that it is easy to do from within the driver, without the game's involvement. In DirectX 11 and earlier, the game cannot interface with the driver in that way at all. That does not apply to DirectX 12 and Vulkan, however. In those APIs, you will be able to explicitly load-balance by querying all graphics devices (including APUs) and split the commands yourself.
Even though a few DirectX 12 games exist, it's still unclear how SLI and CrossFire will be utilized in the context of DirectX 12 and Vulkan. DirectX 12 has the tier of multi-GPU called “implicit multi-adapter,” which allows the driver to load balance. How will this decision affect those APIs? Could inter-card bandwidth even be offloaded via SLI HB in DirectX 12 and Vulkan at all? Not sure yet (but you would think that they would at least add a Vulkan extension). You should be able to use three GTX 1080s in titles that manually load-balance to three or more mismatched GPUs, but only for those games.
If it relies upon SLI, which is everything DirectX 11, then you cannot. You definitely cannot.