That would be extremely hard to do. The State Championships don't make anywhere near the money the Brasileirao does but the costs of running it have no comparison to the same fore mentioned tournament which is why the State Championships are still financially attractive (apart from the footballing aspect).
The best thing clubs like Fluminense, Internacional, Sao Paulo and Gremio can do is forget about a State Championship and Libertores/Sulamericana, go around the world and play other international tournaments. Or at least, partake in many friendlies.
There are many competitions the clubs can take part of. For example: Mexico's cup runs 3 months and that is very doable by any of the clubs we mentioned. Friendlies in the US, China, India and Australia, as preparation for their clubs in the AFC Champions League, are also great ideas. There are many options. Most clubs are too lazy and stupid to do it.