If you define "cope" as 60 fps, no PC with a single GFX card can cope with 4k. Two things will make 4k "ready for prime time":
1. The arrival of the new AU Optronics screens (New models arriving soon from Asus and Acer) which are capable of 144 Hz
2. Video cards that can do deliver 60+ fps in a majority of today's games
Using the 22 games in Techpowerup's game test suite @ 4k, the 1080 Ti with the best numbers
18% of games deliver 45 fps or less
36% of games deliver 60 fps or less
50% of games deliver 67 fps or less
86% of games deliver 76 fps or less
The recommended switchover point from G-Sync to ULMB is about 75 fps.
As for the 1080, it's a great 1080p card, I wouldn't use even @ 1440p.
If you really, really want 4k ... today, I would urge you to at least wait for the new AU Optonics screens. Investing in the older technology today will leave you in a position whereby selling your old screen to get the upcoming technology, will be a tough sale as the value of the current tech will drop precipitously.
To power it, again with currently available GFX cards, and with the anticipation of living with it for 3 years or more, we'd recommend twin 1080 Ti's. Since they have no competition from AMD, nVidia is not exactly putting a lot of effort into SLI since the only result of improved SLI performance is less sales of their hi end cards. But perhaps that will improve once AMD has an entry in this performance niche.