A portion of a Playstation Blog interview with Gearbox Software Multiplayer Producer Chris Brock...

What different multiplayer modes will there be? And how many players are supported in multiplayer matches? (asked by @Pogo_05)
Chris Brock, Multiplayer Producer: We’ve only announced and shown Team Deathmatch at this time, but there are additional modes that we’ll be showing before too long. These modes are more objective based and we can’t wait to put them out in front of people. As far as player counts go, we’re still testing out what feels right on a per-mode basis.

How many maps are there for competitive multiplayer, and how many players does co-op support? (asked by @Nekrospike)
CB: We’re working on many multiplayer maps at the moment. We don’t have a specific number at this time but it will be a good selection of maps that will be our best! The co-op campaign will support up to four players.