More storage in a player's bank box would create a lot more lag. However, a guild safe deposit box would be great. Maybe one with different amounts of storage, so that a small guild might buy 10 slots of storage for 1k gold, 100 slots for 1 million gold, 250 slots for 10 million gold, 500 slots for 25 million gold, 1,000 slots for 100 million gold, and 10,000 slots for 1 billion gold.
As long as they paid the gold, it wouldn't matter whether the guild had 1 member or 10,000. It wouldn't be linked to the player, so there wouldn't be any lag.
Another option would be to rent the safe deposit box. That way, players who just need the room to put all 3,000 of their items in storage for a couple of hours while they re-size their house, or after the house where they had 10 vendors is sold, and the new owner doesn't renew their rental contracts, will have some cheap temporary storage, and people who need massive amounts of storage for longer amounts of time will pay a lot. Maybe charge 1 million gold for 24 hours of storage for up to 10,000 items; most people wouldn't need nearly that much storage, but somebody who had just sold their castle, keep or vendor house would.