Inventory Database & Inventory for a user

So I’ve got a unique, but probably not so unique, issue.

I’ve got a site obviously using WordPress. I’ll be using BuddyPress to have some accounts and profiles, but what I need to figure out how to do is make an inventory of items for each of these accounts.

Basically, I want to have a database of items. This database would be searchable, and would allows users to add these items in the database to their own personal database.
I was hoping there would be a good plugin or something to manage this. I assume I could do it with WooCommerce, but I guess I might have to do a lot of code work to make everything work right (change names of “Cart” to “Inventory”, make those items stay in the ‘carts’ indefinitely).

Is there anything that can help me achieve this? Or do you guys have any suggestions to make this easier?