You can run 6 GTX 1070's easily with -25% TDP (125W per card) as the only config change. I have two rigs running this way nicely, each makes anywhere from $20-$40 a day depending on the market. They run nice and cool this way as well, just need to good open air rig. GTX 1080's and Ti would work as well, but I have no personal experience with them and there are a few on the forum here that can comment better on those.
My 3-card "hybrid" 1070 rigs pull about 600 watts at the wall on a good gold PS despite pushing a top-end AMD A10 cpu hard on the GPU side.
A 6 card "mining-specific" rig should be QUITE comfortable on a Seasonic X-1250 gold/X-1200 Plat or an EVGA 1300 G2 / 1200 P2.
You could probably go with 1080 cards instead of the 1070s, if you keep the power limits down some - at least some 1070 cards (Gigabyte in specific) change the TDP to 180 watts in order to be able to support their higher clock rates, my Gigabyte 1080 card TDP is only 20 watts higher.
The 1080 ti needs *2* PCI-E connectors (one 6-pin one
per card - there are exactly ZERO power supplies in the under-1500 watt range with enough PCI-E connectors to run 6 of those cards (and I think you have to go to 1600 watt power supplies to get to 12+ connectors) - which doesn't factor in whatever you have to use to power your risers.