Here are all of the Pokémon Rumble Rush Rank and Island Rank Rewards
As with most titles, Pokémon Rumble Rush on iOS and Android has its own ranking system that rewards the players will items as they play the game.
As you level up, you will either unlock ten new Pokémon storage spots or receive Power or Summon Gear Slots as well, boosting your inventory capacity.
Whenever you level up to an even number, you will get 10 Pokémon slots; every odd number level up will be Power or Summon Gears, when you reach level 10, 20, 30, etc. and onwards though you will receive 10 Pokemon slots and 50 Power Gears each time.
The leveling up of ranks maxes out at level 50, so there is a limit to the number of freebies you can get. Granted, getting to level 50 is a slog at best anyways.
On top of the game's core ranked system, there is also an alternative ranking system known as "Island Ranks" that are rewarded after you defeat a Super Boss on an Island.
As your Island Rank increases, some things alter in-game, such as the available CP of Pokémon in the wild. It can also affect the Ore you can collect as your rank increases.