This concept was used in some of the first RPG sessions ever played, the “Braunstein” sessions. There could be a merchant trying to escort his goods to town, a thief trying to steal the goods, and/or a political revolutionary trying to blow some government building up.
This seems fun, so I thought up some bullet points for how this might work:
Make players pull roles, along with their corresponding goals, out of a hat.
Make more roles than there are players, adding an element of surprise for you, the GM.
Make people reveal their roles to you, but not to the other players, making it more interesting and realistic.
Make roles that could easily conflict with each other, as well as ones that could cooperate, like the thief and merchant mentioned earlier, or a knight and a noble.
This would probably work best in a somewhat small sandbox, like a small town.