What's the max box storage for broke players?

I recently started playing champions since it released on mobile. I've reached greatball tier in 3v3 and noticed that it barely increased my poke storage. From what I've read, you can increase it again by climbing higher in rank. What I was wondering though is if you could get each storage upgrade twice by climbing both in doubles and 3v3. I haven't been able to tell so far since the collection of poke I have is trash for doubles. I've been spamming the encounters to get Whimsicott which is my favorite VGC poke but I haven't got it yet.