Multiclassing a barbarian and wizard

As others have said, unless it's homebrew, you can't go above level 20 - regardless of how may classes you mix and match. Wizards get their first and only 9th level spell slot at level 17, so going Barbarian for more than 3 levels will lock you out of it completely - which means no Wish or True Polymorph. Furthermore, as the two classes don't really mesh well (in terms of maximizing your efficiency), it'll be a very MAD combo and thus you'll probably be under-performing in both roles - depending on your DM's style and difficulty of their encounters.

Going pure Wizard will eventually allow you to warp reality, assuming you reach the higher tiers. Dipping in Barbarian might make that harder. However, if you're really in love with this concept, I'd suggest looking into some guides - as by now folk have brainstormed all manner of multiclassed concepts.

/r/DnD Thread