(Most of) NVIDIA's AIB partners have been flooding out announcements of custom GTX 1080 designs. Looking over them, it seems like they fall into two camps: one believes 1x eight-pin PCIe power is sufficient for the GP104, and the other thinks that 1x eight-pin + 1x six-pin PCIe could be useful.
ZOTAC, on the other hand, seems to believe that both are underestimating. Excluding the Founders Edition, both of their GTX 1080 designs utilize 2x eight-pin PCIe connectors. This gives their cards a theoretical maximum of 375W, versus 225W of the Founders Edition. At this point, considering the Founders Edition can reach 2.1 GHz with good enough binning, I'm guessing that it's either there simply because they can, or they just didn't want to alter their existing design. Not that, if you only have 6-pin PCIe connectors on your power supply, ZOTAC provides the dual-six-to-eight-pin adapters in the box.
The two SKUs that they are releasing, again, apart from the Founders Edition, vary by their heatsink. The ZOTAC GeForce GTX 1080 AMP has a dual-fan IceStorm cooler, while the ZOTAC GeForce GTX 1080 AMP Extreme has a triple-fan IceStorm cooler. (IceStorm is the brand name of ZOTAC's custom cooler.) Other than the 2x 8-pin PCIe connector, there's not much else to mention. ZOTAC has not settled on a default base, boost, or memory clock, and you will probably be overclocking it yourself (either manually or by using an automatic overclocker) anyway. Both cards have a back plate, if that's something you're interested in.
Once again, no pricing or availability. It shouldn't be too long, though.