The 1 inch of fish per gallon rule is out. There is no general rule currently, you just need to do the research of the fish you want to keep. A good place to start is Badmans tropical fish website (which I've given you below). The minimum tank size is listed for the individual species.
You really can't increase the carrying capacity because there's only so much space and oxygen. Even if you added an air stone and live plants, you would still run out of swimming space. Also, the with more fish you would have more ammonia which is the number one fish killer, and it kills fast. If you put more fish in the tank, you would need to do more water changes which would stress your fishes out. This could lead to serious diseases. However, when I figure out how many of what fishes I can have in a certain tank, I still want to provide an air stone or two because with tropical fish the water temperature has to be warm, which doesn't hold as much oxygen. I always give them more oxygen because with more than one fish not only are they competing for space, they are competing for oxygen.

Does this answer most of your questions?
Badmans fish


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Phishie

"An ounce of prevention is worth a pound of cure."

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