The CRB is rather restrictive about it:
Spells: A sorcerer casts arcane spells drawn primarily from the sorcerer/wizard spell list presented in Chapter 10.
Now this list was expanded by other books, and there is the "unusual spells that the sorcerer has gained some understanding of through study" loophole. A GM can allow you to learn a new spell that's basically empowered magic missile.
However, it's usually not a good deal. Sorcerers have a very limited amount of known spells already. With spending a precious known spell on something that could be done via metamagic you cut down your versatility, in favor of a (tiny?) advantage in action economy. You could have learned fireball, haste or fly instead, to stick with the 3rd-level example...
So what's your intention? Do you want to stick with magic missile as your primary spell?