There are many ways it can be done:

1.) Blue Mage Classic ignores the current ability list patterns and just learns abilities whenever, and has an unlimited number of possible abilities. It just keeps adding new abilities to the list, and they can all be used at any time.

2.) Blue Mage XI gets a new blank slot instead of an ability that it can fill with one of the monster abilities that it's learned. Abilities are learned permanently, but only a limited number can be set. As a Class, this version can set up to 17 abilities. As a Job, it can only set 5 at a time.

3.) Blue Mage Riot (because this version would cause players to riot) learns abilities temporarily and has a limited window to use the ability before it's lost. Blue Magic would be a counter-attack like Haymaker or Shield Swipe, but using the enemy's own ability back against it.

4.) Blue Mage Suck learns a specific few iconic Blue Mage spells, learns them by levels like anyone else, and can't learn new spells until the level cap is raised. It's passable as a Class. It would be the worst Job.