Identify Business Unit associated with a customer site

Summary:

How to identify Business Unit associated with a customer site.

Approach-1:

1)Define a custom Reference Sets each for one BU
2) Attach Reference Set to each BU
3)Then create different customer site for each new reference data set

or
Define Reference Accounts at Customer Site level or Transaction Types and attach to each BU. Again hurdle here is all the BU's would be listed so hard to identify to which BU customer site belongs to.

The problem is if there are 10 BU's we have to create 10 reference sets and attach to 10 BU's. Please suggest any feasible approach that's applicable.

Do we have any REST API's to update the reference set at the customer site?