Local or Online?
the answer is of cource PS4 will, but in the end it's really up to the developer. Local split screen seems to be going away in favor of MP COOP more and more, but some titles still try to put it in.
Twisted Metal (PS3) had 4 player local split screen for example.
Online, Borderlands comes to mind this Gen. Next gen Destiny looks to me 3-4 player local COOP with “world events” that will pull in many more to help you battle large numbers of people. Ubi’s The Division showed off 4 player vs AI COOP, then hinted at PVP at the end in the same world.
If you’re looking for a good reference site with a focus on COOP, here’s the best I’ve found: http://www.co-optimus.com/