In order for multi-sourcing to be successful, organisations must be capable of integrating their service providers into a single, cohesive unit.
SIAM/MSI - An introduction to Service Integration and Management/Multi-sourcing Integration for IT Service Management explains:

• the merits of a multi-sourced approach to outsourcing service towers
• the benefits of multi-sourcing contracts with service providers for specified towers
• how to align multi-sourced services
• the challenges of using a multi-sourced model
• how to determine the IT operating model (with reference to the international standards ISO 38500, ISO 38501 and ISO 38502)
• the different types of service integration models (ISI, ESI and ETSI), and the benefits and challenges of each
• aggregating service-level performance
• a multi-sourcing RFP approach, taking into account structural, operational and governance requirements.

If you're thinking of moving from a single-source to a multi-source outsourcing model, SIAM/MSI - An introduction to Service Integration and Management/Multi-sourcing Integration for IT Service Management provides the answers to all of your questions.
David Clifford is a director of Pace Harmon, an international advisory firm headquartered in the USA. He has contributed to a number of publications about IT service management, writing about ITIL(R), service agreements and international standards. He also initiated, and contributed to the development and assisted with the promotion of EXIN's IT Service Management qualification program based on ISO/IEC 20000. He is currently Chair of the BSi committee on IT governance (ISO/IEC 38500) and contributes to the development of the IT service management standard ISO/IEC 20000 and BPO for IT enabled services (ISO/IEC 30105).