the Jester
Legend
You can do that without having ability modifiers tied to background, though. You just assign one of your high stats to Strength.For example, in my example in the post above, the Elf Wizard character with a Soldier Background, takes advantage of the official permission for the player to create ones own Background. The result is an individuating character concept: a high Strength Wizard, a Fey, being tutored in wizardry by a primordial Elf, speaking Celestial, with combat experience in the High culture fighting style. This Elf is "more unique" than other Elf characters. Being "different" is part of being "unique". More customization makes this individuation possible.
I feel having "my character knows one of the most powerful wizards in the multiverse" is a bit presumptuous, and a bit special snowflake, for my tastes; but if you're going to do it, you don't need a special background at all, you just make it part of your backstory (assuming you have the DM's buy-in).The Background is more than the sum of its mechanical parts. It is especially the narrative circumstances during which the character acquires these mechanics. These narrative implications can be highly relevant in certain encounters, and unique.
For this character, gaining level 1 in the Wizard class is about the most standard mechanic possible. But saying that the character reached level 1 by being tutored by one of the most powerful Wizards in the multiverse is something remarkable − campaign altering.
If you want to know the most powerful anythings in the nation, much less the multiverse, you should- at least in my game- seek them out in play, not assume that you did it before you even start play. That is similar to the pc who wants "I was a great hero and general in the last major war" or "I'm the kingdom's heir" as part of their backstory. Unless the DM is willing to go for it, those are the kinds of things that happen through play, not before play.