Cloud service providers benefit from a vast majority of customers due to variability and making profit from commonalities between the cloud services that they provide. Recently, application configuration dimensions has been increased dramatically due to multi-tenant, multi-device and multi-cloud paradigm. This challenges the configuration and customization of cloud-based software that are typically offered as a service due to the intrinsic variability. In this paper, we present a model-driven approach based on variability models originating from the software product line community to handle such multi-dimensional variability in the cloud. We exploit orthogonal variability models to systematically manage and create tenant-specific configuration and customizations. We also demonstrate how such variability models can be utilized to take into account the already deployed application parts to enable harmonized deployments for new tenants in a multi-cloud setting. The approach considers application functional and non-functional requirements to provide a set of valid multi-cloud configurations. We illustrate our approach through a case study.