Is there a way to add a Business unit in searching a Project Number in all Project Number Fields?

Our Clients are with Intercompany process, and they are allowed to use other BU projects on their transactions.

But on entering the Project Numbers (or Searching functionality on Project Number), it only has Project Number Value and Project Description Value

on search functionality in all transactions (Like Expenses, AP Invoices, OTL, etc).

Can we add value on search like "Business Unit" of the Project as it will be a great addition on identifying from what BU they are charging?

Even it is in advance mode search, the Add fields will only add Value and Description only.

Thanks!