1.) multi-classing. The Level 12 cap is class-based, so after reaching 12 in a single class you can always begin taking levels in other classes.
2.) feats. Level "13" fighter would be your level 12 Fighter plus appropriate HP Increase, Applicable Proficiency Bonus Increase, and you get a Feat to compensate for the lack of implemented actual level 13+ Fighter Abilities. Spellcasters would get new spell slots but no higher level spells, along with the stuff mentioned previously.
While it makes perfect sense and seems like good solution ...
I really hope Larian will not go this route. :-/
There is no real argument against it, just my personal prefferences ... since i really dislike multiclassing, and it seems to me that it is allready done wrong in many games (tabletop included) ...
Since, the whole idea of multiclassing (at least as i see it) is that you sacrifice some high-level features of your Class in order to get something else ... and this model is good and i really like it.
For example pure Barbarian gets feature that allows him to boost his Strength and Constitution up to 24 both ... and that is AWESOME ... therefore there is a question if sacrificing this, in order to get for example Second Breath and Action Surge from fighter is worth the cost ...
Sadly, most games (tabletop included) dont reach level 20 ... meaning this Barbarian would never reach this bonus anyway ...
So if the game ends in level 13 ... all you would loose is one Ability Score upgrade, and one Dice for Criticals ... still kinda good bonuses, but in my honest opinion not nearly so shiny and tempting as +4 to your two most important scores and raising their cap.
And thats what i dislike, its this "all benefits, no drawback" that seems wrong. :-/
And if we would get up to level 12 per class, but the game would allow our characters to reach level 15 ... we only get even deeper in that. :-/