Can I start a new game in Borderlands 2 but use an old character?

I have a character I made with a friend playing 2player. I want to know if I could start a new single player game and import that existing leveled up character with equipment into the new game like you could in borderlands 1.

Solution 1:

There are basically two options here:

1. Just have the person with the least quest progress start the game. Story progress is tied to the host, so if you join a level 1 person starting the game you can progress through the story as if you never have before (you won't get quest rewards for stuff you already did though).
2. Reset quest progress in Ultimate Vault Hunter Mode. This will let you completely reset quest progress and start over again. Unfortunately you and your friends must be at level 50 or so to be able to survive UVHM and at least one of you must have UVHM unlocked.

There's no real way to reset your own quest progress outside of UHVM though, just like there wasn't in BL1.

Solution 2:

Just goto select character from main menu and when it asks you what game mode you want (such as true/ultimate vault hunter mode) you just press triangle to select the reset option to reset all mission progress and restart the game from the very beginning as a (say level 61) existing character.

Solution 3:

Each character's quest progression is saved "inside" that character, and you can't reset it. When you play together, the party is doing quests that game's host has active, but quest progress is saved for everyone.

If you have completed some quest - in any game, solo or team - this quest is done for you, and you can not redo it. There is an option though - someone other than you can do it, taking you along. I.e. you can join a game of a brand new character and play through everything again.

Obviously, you will be able to experience the story again in True Vault Hunter Mode - Normal and TVHM are distinct "save slots".

So, if you want to savour the story without anyone interfering and cannot create a dummy character just for that - you are out of luck.