How much power do you need?
If you upgrade to a second 1080Ti you will need about 250W*2+150W of power supply, plus peripherals, plus enough to catch any power usage spikes and to compensate for the sub-100% efficiency and the efficiency degradation over the years. So 1000W is a realistic estimate for this (and a comfortably conservative one).
So what is the recommendation?
The EVGA SuperNOVA 1000-G3, it is an ATX form factor 1000W Gold-rated PSU with 8x 8-pin connectors for graphics cards (you will need 2 or 4 of these).
So what are the differences between Titanium, Platinum and Gold PSUs?
The difference between the various certifications are efficiencies. A Titanium rated PSU needs to hit 94% efficiency, a platinum 92% and a gold one 90%, so as you see there isn't that much of a difference. However, as you have such a large buffer with regards to power, going with a gold-rated one will do.
Additionally EVGA is extremely confident in the quality of this PSU, which is why they give a decade of warranty on it, so I wouldn't worry about build quality (and besides EVGA has an excellent reputation with power supplies).
If you want to read more about PSUs, have a look at this article (about this PSU) and the references it links. And also note that Mark's suggestion will also be fine (and a little more efficient / with a little longer warranty for a bit more money).