Cross-cloud is a strategy followed by organisations to use services provided by multiple cloud service providers. To provide a seamless experience, IAM interoperability issues need to be addressed. Current approaches involve relying on a third party cloud broker which causes known-problems that originally led to the concept of cross-cloud. In this article, we analyze the IAM interoperability issues when building a cross-cloud environment on top of the current major cloud service providers (Amazon Web Service, Microsoft Azure and Google Cloud Platform) by implementing a cross-cloud storage application. This experiment demonstrates the need to integrate new identity management systems to cloud IAM services in the future. We then propose a cross-cloud identity management model that follows the Self-Sovereign Identities principles and which is interoperable with existing cloud IAM services.