All longhaul flights will do this. They all take cargo, ranging from some bulk freight to multiple tons of ULD loaded cargo. If you are early at the gate you can see that when looking to the right hand side of the plane. Those containers do not only hold the luggage. Some freight is excluded from this kind of operations as they are classed Cargo Aircraft Only (CAO).
And sometimes they make it a full freighter flight (no pax in cabin). AY has done this for some time with an A340. It just comes down to economics. Some freight will bring enough revenue to support this kind of operations
So, nothing prevents them from doing so. Except when they do not comply with organisational requirements (paperwork, crew training).
And for the capacity: Cargo aircraft have a lighter set-up as they are not carrying the chairs and other amenities provided in passenger planes. So they will always have an extra weight advantage compared to pax configured planes. And for non-pax operations with passenger planes the max loaded weight per position is the determining factor if it ain't cargo seize.