The only ones that come to my mind are the Sanctum
games and

Dungeon Defenders.

Edit: (Posting multiple links seems to be seriously borked right now.)

4 players? That's a pretty rare one. Swords & Soldiers is good, but 2-player only.

Sanctum 1 + 2 is a series of first person tower defense games with 4 player co-op campaign. Unfortunately STEAM only...

EDIT: Also Iron Brigade(which is frequently 90% off on STEAM or HumbleBundle Store, so you should wait for a sale and save a lot).

I disagree ;-)
Most Tower Defense maps for Warcraft 3 support up to 10 players.

Isn't multiplayer tower defence basically what MOBAs are?

I've never actually played one but I got the impression that was the idea...

To some degree. In MOBA games you're supposed to defend your main structure from being destroyed but it's not the main goal and the gameplay is very different from TD games.
In tower defense games you are placing all sorts of defensive structures in order to prevent waves of attacking units from reaching and destroying whatever you're supposed to protect. Placement and management of those structures is the core mechanic in TDs and it's something you don't really have in MOBAs. (Well, at least it's how I see it.)

No they're not the same. There are similarities but they are quite different.

In fact I don't think there can even be such a thing as a multiplayer tower defence game. There can only be a co-op tower defence. Unless the OP meant DOTA/MOBA but incoreclty called it tower defense.

EDIT: The more I think about it, the more I realize that the only way you could design a multiplayer tower defense game, would be by making a MOBA, except that you would also have the ability to build various types of towers to grind the creeps.

Ah, so you don't actually build or place towers in MOBAs? I thought that was an element of those games.

In that case yes, a MOBA with tower building is basically the only way I can see of doing competitive multiplayer TD.

No, in MOBAs you have only control over your hero unit(movement, triggering your abilities, and level up development).

The vast majority of TD games don't even have a hero unit. They function more like sim/management games, you build your towers and then you allow time to pass, while you gather currency to build more towers/upgrade towers/replace towers with better ones.

However this is becoming less frequent in an attempt to differentiate and introduce a more involved gameplay.

Competitive tower defense already exists, and is not really related to MOBA ;-)

Each player plays in its own area, build towers and earn gold by killing creeps as usual. But there are two ways to spend gold: buying towers (of course) or buying creeps to add them to the next wave spawning in your adversaries areas.
The winner is of course the last player standing.

Some games to spice things up will make the next wave spawn as soon as one player killed all of the creeps of the current wave, even if the other players are already struggling with the current one.

Never heard of than. Sounds more like a party game, than an actual multiplayer game. Like playing PuyoPuyo or Tetris in party/versus mode. Each player plays a separate game of puyopuyo/tetris, and each time you clear a group/line you force a detrimental effect upon your opponent. The game ends when a player loses naturally.

What titles are there?

Team Fortress 2. Play it as an engineer, then it is the best tower defense game ever. You are welcome afterwards.

Sanctum 1, 2 and Orcs must die 2

The ones I’m thinking about were all Warcraft 3 maps, before stand-alone TD really became a thing on their own. Sadly I didn’t play any of them for years now and can’t remember their name.

But in the late 90’s early 00’s we played this kind of games a lot with friends on LAN, along with Medal of Honor (before it gave place to Counter Strike) and a couple other games that were really hot at the time ;-)