Can you set-up multiple AR Cash off-sets for fund?

Our organization is going to be starting a joint venture with another organization.   We will have customers that will have invoices issues from both our home organization and the joint venture.  We well be setting up a new Business Unit for the joint venture.   These companies that are in both are likely to pay for both of their invoices with one check.   We have been able to create a deposit and apply it to both invoices in the separate business units.   The problem is when we create the interface from AR to GL there is only one AR off-set.   We