Only bilateral series is happening now. Triangular and quadrangular series have all but died out. There is no room available in the packed international calendar to schedule multi-nation tournaments apart from ICC trophies. The IPL franchises on the other hand are not contended with the two and half month window available for them and want to expand outside the Indian market so that they can continue playing all through the year. But when the same set of owners take ownership of multiple franchises, there needs to be some overlap in players, so that the fans will continue to support all of their teams. Right now, there is no such overlap. For example, KKR in IPL and Trininbago Knight Riders in CPL are having same set of owners. But there is hardly any player who feature in both the teams.
For the better future of this game they need to work on franchise because now it's future but need some good system and rules which never hurt others with this they can go ahead like UEFA is going, and they are currently one of the best system with good fan base and too much money around them.
ICC is authority which can bring them on table for fair rules and better management because these things are very important even Indians are going to control few leagues around the world but still few countries are going to have things which will be not under their control and this can create conflict which could be never been healthy.
Right now BBL, Vitality Blast, BPL and PSL are having not Indian connections which mean they also need some better treatment from ICC for good future just IPL is having special treatment is never been fair.