How do others manage contract invoices when the sponsor changes within the project period?

Summary:

I'm interested to learn on how other entities manage when they have a contract setup with a contract research organization (CRO) site and then the sponsor changes to a different CRO site. We can't change the name or address associated with the original CRO site as we have other arrangements with that site for other projects/contracts. According to details I learned from our implementation partners, Google searches and trying myself, we can't change the sponsor once a contract is setup. The CRO site change is not a unique situation to us so I'd like to know how others manage in