I have the game and all of its DLC. I am at level 18 in the single-player.
Do you suggest that I finish the single-player before starting multiplayer? What are Borderlands' multiplayer features/game modes?
The main Multiplayer mode is co-op.
I would level as co-op from now on. It's very fun (up to 4 players), mobs become more difficult and loot is better.
What is nice about co-op is that each player continues to play in their own story but you all play together (for example 3 people help you on your Quest xy but they already did it).
As far as I can remember, the player's game with the least progression is always the game the other players will also play in.