I'm not so sure. The easiest way to load them would be through the ports, and all that's required is something to align the loading tube with the storage tube, make the connection and gently push the torp over. Surely that would be possible underwater, and fully automated as well.
If torps are made to swim out, then you could have a rail system inside the storage tube, so that when the first torp is away, the next in line is moved forward to the launch position. If the sub itself is 400 ft long, for example, the storage tubes could maybe be 250 ft, and that's eight torps in line. Imagine three such tubes stacked vertically on each side... 48 extra torps. Not sure how that would work with regards to buoyancy, though.
Added a simple illustration. The big black circle is the pressure hull, and the grey is the outer hull, with the six black circles as torp tubes. This would be for a new hull design, though.
