Most fantasy Wizards can do anything unless they can't, lol.
Even if they claim to not be able to do something because of "da rulz", you can be sure someone in the story will do something "impossible" to flex their power and style on lesser casters.
Examples include: spellcasters from David Eddings books like Belgarath, spellcasters from The Wheel of Time (we're told there's stuff men can do that women can't, but it's a bit shaky; the main problem with using magic is men go crazy), spellcasters from The Sword of Truth (technically, some Wizards can only "add" or "subtract" things with magic, but there's a lot of clever workarounds, and there are characters who can do both), and, of course, Wizards from the Harry Potter 'verse, who can learn any number of spells, even make their own spells, and can fire off spell after spell without seeming to get tired (with masters being able to use spells without incantations or even wands!).
There are exceptions, like Skeeve from Myth Adventures, who has a limited repertoire of spells, but has a lot of practice at using them, and occasionally runs low on "magic juice" to power them. OTOH, the only thing really stopping him from learning new spells is time (which his life gives him precious short amounts of).
I'd mention Rincewind from Discworld, who is a really terrible "Wizzard", but he has other things going on for him.