I would assume they would add additional pages to the vault, as it works with your friends list and currently players list.
Another possibility is that they could split the vault into three different vaults. One for inventory items, one for weapons, and one for armor.
EDIT:
Many thanks for all the replies and opinions!
Can we make it to the trending page??
-
Why not have bungie create extra pages for vault storage that you can scroll through with R1 like scrolling through your inventory? That way you can have 20 slots per page and have like 20 pages....problem solved