.Concerning the technical side of things:
Battlefield had somewhat a big development team, but not all of them were working on the network side of things
.You can achieve something like what you want with a decently big enough map and good map design, and game mode design.
The biggest problem in multiplayer games with tons of people (let's say 64) is synchronizing everything between all the players.
The trick in doing these kind of multiplayer games is making sure a small amount of players are relevant one to another at any given point. Let's say that from the 64 on the map, you rarely see 16 at a time. So the rest don't need to be synchronized to you, because you don't care what their position is or what they are doing at a certain time. They will become relevant to only if they shoot you or get in a certain range, or satisfy some other conditions.
Beyond this main point you also need to hide the lag between players, having a nice prioritization system ,etc.
You could look into commercial engines(Raknet had some interesting api, I did not work with it directly, but rumors say it's nice), Unreal Engine has some surprisingly nice network capabilities, not as fancy as the ones from valve where they rewind time on the server but cool nonetheless.
Or you can get a coder to work day and night on this
.As a positive and non depressing example I'll give you Mount and Blade. They have servers with up to a hundred players(sometimes more), with a quite high density of players in a map (unlike battlefield 3 where your team of 32 is spread among a huge map), and the multiplayer feels pretty nice. Keep in mind when comparing to valve's or Bf3's multiplayer or that Mount and Blade was made by a ridiculously small team of people.
