For a breaker to allow two wires it must be rated as such. You'll often see a picture with two wires if allowed. Typically its never allowed for aluminum wire. Occasaionally local codes don't allow it even if the breaker does. Another potential solution is use one wire to the breaker, but then splice in another a few inches away. If the box is not too cramed, this will work, just use the correct size wire nut. Another solution is a tandem breaker, which is basically two breakers in the space of one. You do this if you don't have more breaker space.
If you do have breaker space, just add a new breaker. That's always allowed and the best solution of all if you have room.