Just curious if this is possible without a mod. PS3 user here. I'll live with what I have picked up to level 26, but I just wanted to know if it was possible. Searching all over google but not having much luck since all the results are from when the game was released.

Nope, you choose a perk and you have it for the rest of the game with no back backsies.

Would be a cool idea to have a perk in Fallout 4 that when you reached the max level you could choose a perk that allowed you to rechoose all your perks again.