Aintree University Hospital NHS Foundation Trust
The trust’s website  says that private patients are treated by Abbey Sefton Hospitals:
Abbey Sefton Hospitals are the Private Patient provider for Aintree Hospitals NHS Foundation Trust. They have a separate ward located on the University Hospital, Aintree site. All private patients must be booked through Abbey Sefton Hospitals, usually by the referring consultant.
In the Annual Report  the trust lists two future joint ventures:
The joint venture for laboratory services and the model for a combined vascular service are currently approved in principle. The vascular changes are currently awaiting the outcome of a regional public consultation.
These were in addition to its existing subsidiary, Aintree Healthcare Limited:
In July 2007, the Trust established a wholly owned subsidiary company called Aintree Healthcare Limited. The purpose of this company is to provide community healthcare projects. As at 31 March 2012, the company had not commenced trading.