I know we have met a few people with a few types, but they tend to relate and many mages stick to one kind.
I mean I know Dragon Slayers have their own set of rules going, but Mashima has never dictated that if other magic is a straight up a hereditary thing or not.
So could Lucy learn how to use Cana's cards since they are both object mages? Or is these something that prevents her from that? But on the other hand she was able to use Urano Metria, a caster spell, which was unusual.
Why don't mages learn a bit of healing magic or something similarly useful; even if they can only use these spells at a limited low level they would help a little bit.
So what exactly is keeping one mage from learning other magic? Is it just plot? Easier to study just one?