It seems that it only has 2 player split screen for it.

Kino der toten and Five are the two Zombies mode maps and they only have 2 player split screen (although you can do online splitscreen)
There is a third zombies mode that plays more like an arcade shooter (think smash tv or geometry wars) and that is 4 player local though.

Some people have spread rumors about being able to get it to 3-4 player split-screen. however, none of those rumors have ever been backed up with evidence.

its 2 player split screen for the classic zombie modes, and up to 4 players for dead ops arcade.

I submitted this as a glitch it has yet to be accepted but here u guys go in advance....
Have 4 people signed in and load a game of "dead ops arcade". While the game is loading player one needs to sign out. The game will go back to main screen. Go into zombies and it s...hould say 4/2 if the glitch worked. If you want to play "five" just sign player one back in if he has "five" unlocked. NOTE: I just discovered this glitch and have yet to do extensive testing but in our first couple runs the only thing we've found to freeze the game is going into a teleporter, so just avoid those and u will be good to go.

Write to youtube "Call of duty black ops: zombies 4-player split-screen" My account is Teenuxxx! there is evidence that is works

Wat all split screen modes are there

2 players Maximum for offline mode , and i know it sucks -_-

It's only two player local but if you system link you can play 4 player on zombies

There is only 2 players allowed, and they did have 4 player rumors, although they did not turn out true. but you can also play 4 player over PSN PC connectivity or across Xbox Live.

You can only do 2 player split screen on one console but if you want to play with 4 people you can system link with someone else but even then it would be 2 people on one console and 2 on the other console

Four player over system link.
But only Two player split-screen.
Pretty wack.

I follwed-up on Teenuxxx and checked his Youtube, from the instructions that he gave on how to glitch the game so you can play 4-Player Split-Sccreen in Zombies.

there IS 4 player offline split screen, i did it before. its a glitch. search it on google,
"black ops 4 player split screen zombies". it should show up a youtube link on the tutorial. it actually works, which is pretty cool. im thinking that treyarch put this as a "secret", otherwise it'd be impossible, or it'd be done in WaW.

Yes. It works lol.