You are able to play through the levels in Quake II remaster cooperatively with other players. To see how you can properly do so in the first-person shooting videogame, you can check out this article from Seeking Tech.
How to enable co-op mode
In order to enable cooperative mode in the Quake II remaster, you need to take the following steps:
1. Select Multiplayer from the main menu.
2. In the Multiplayer screen, you should see the number of controllers connected. If you are playing with others locally, make sure you connect any other controllers you have before you select the Continue option.
3. On the next screen, you can choose to play Local, LAN or Online.
4. Eventually, you should see a screen showing the next match type. Here, you need to select the “Change settings…” option.
5. In the next screen, change the Game Mode to Cooperative.
6. You should then be able to select the Episode, Map and Difficulty.
7. At the bottom of the screen, you can also change the following customization options: Respawn on Squad, Enable Maximum Lives, Maximum Lives, Extra Enemy Health Percentage. Friend Fire, Instant Weapon Switch, Player Collision, Allow Grappling Hook, Infinite Ammo.
How does respawning work in Quake II remaster?
In order to respawn your teammate in co-op mode, you need to do either of the following:
1. Clear out all of the enemies in an area.
2. Find a safe place where there are no nearby enemies.
Once the game detects that you are in a safe zone, then your teammates should respawn next to you if you have the “Respawn on Squad” setting enabled previously.