Here comes Grrraint getting things wrong again...I hope I never have to step into a house you build...
For the benefit of you and the OP this is how footings work:
For the sake of argument, let's say the soil has a bearing capacity of 100kN/m2, and there's 50kN/m load at the base of the wall. A 450mm wide footing won't be enough as:
50kN/m / 0.45m = 111 kN/m2 which is more than the allowable 100kN/m2.
So if we make the footing 600mm wide:
50kN/m / 0.60m = 83 kN/m2 which is less than the allowable 100kN/m2.
If you leave the footing at 450mm wide and make it deeper, it's not going to make a blind bit of difference to the spread of load (except for allowing the load to spread under openings such as French Windows or Patio doors).
Footings are made deeper for a number of reasons, but it's rarely got anything to do with the load on them.
They can be deeper to ensure the base of the footing is below the tree zone of influence, or to prevent frost heave.
It's possible that digging deeper might get you to a better bearing strata but that wouldn't often be the reason for digging a deep foundation.
By the way, building on the edge of a footing will load the footing eccentrically and could cause an uneven distribution of forces at the base.
You probably could build a house with a loft conversion on a 450 wide footing but you'd want to be sure of the load distributions and the capacity of the soil or you might come unstuck...