Few days ago I thought about a Synchronize Box Item, that'll be used to store the Synchronized Pokemon.
In my opinion, it could be useful and save a lot of time when you don't have the Subway system, or just like when you just want to switch your synch' pokemon when the game-time changes from Day to Night.
In order to illustrate quickly my idea, if you want to hunt Gligar on Route 227 with an Impish sync' and get it, instead of backing towards the Pokecenter you just open your Synchronize Box Item and change your synchronize pokemon.
I also thought about the way to get this Synchronize Item, here are my several ideas about it :
Secondary Quest : Get all the non-neutral Synchronize (OT only or no). The NPC will not reward you from the Synchronize Box until you haven't show him all the Synchronize Pokemon
Crafting Item : Gather certain kind of objects / fragments, and fuse them into that box.
Reward : Could be a reward from the Celadon or Solaceon Quest, requiring 150+ IV on the pokemon, randomly generated
I also thought about it because I lose some times backing to Pokecenter to look for another Synchronize pokemon that I can't search fast. I think about people that have difficulty to reorganize their Computer.
I hope my idea has been clear enough, and for any question or any point I haven't mentioned, don't hesitate to ask me question so I can offer further reflexion and information if so.
Thanks for reading :)