How can I play Pandemic with 6 players?
I haven't seen recommendations for six-player, but I can't think of a reason it can't be done. I think the only thing that needs to be decided is the size of the players' starting hands. 4 and 5-player games start with two cards. You could either go with two or drop it to one. I'd probably stick with two. Beyond that I think you can just play. There's nothing in the game that will break by having six people.

That said, I'm not sure how well it will play. The consensus is that the game gets harder with more people, but fortunately it's very easy to tweak the difficulty in Pandemic. You can decrease the number of Epidemic cards, increase the Special Event cards, or allow players to choose their role, each of these will make the game easier to beat. 

If I were going to try it, I'd probably go with two cards for the starting hands, four epidemic cards, and I'd put all 13 Special Event cards in. I'd see how that goes and then tweak it from there.