Declarative approaches for automating the deployment and configuration management of multi-component applications are on the rise. Many deployment technologies exist, sharing the same baselines for enacting declarative deployments, even if based on different languages for specifying multi-component applications. The Essential Deployment Metamodel (EDMM) Modeling and Transformation Framework allows to specify multi-component applications in a technology-agnostic manner, and to automatically generate the technology-specific deployment artifacts allowing to deploy an IaaS-based application. In this paper, we propose an extension of the EDMM Modeling and Transformation Framework to PaaS and SaaS by allowing to deploy application components on PaaS platforms or to implement them by instrumenting SaaS services. Given that not all existing deployment technologies support PaaS and SaaS deployments, we also propose the new EDMM Decision Support Framework allowing us to determine which deployment technologies can be used to deploy an application specified with EDMM.