Going beyond noble djinn and efreeti, there's the solar with a per day and two demons with a per week and per month respectively in core. If you assume limitations separate them and like abilities are the same, that's 3 from a genie, 1 from a solar, and 1 from a demon for a possible total of 5. Even if you think they are all the same ability, that's still 1 wish without restriction and up to 2 more with restriction for a total of 3.
I remember reading in a faerun book that by default SLAs are arcane by default because they draw on the power of the weave. Maybe there's something in a setting specific book?