Elasticity is considered as a fundamental feature of cloud computing where the system capacity can adjust to the current application workloads by provisioning or de-provisioning computing resources automatically and timely. Many studies have been already conducted to elasticity management systems, however, almost all lack to offer a complete modular solution. In this article, we propose MODEMO, a new elasticity management system powering both vertical and horizontal elasticities, both VM and Container virtualization technologies, multiple cloud providers simultaneously, and various elasticity policies. MODEMO is characterized by the following features: it represents (i) the first system that manages elasticity using Open Cloud Computing Interface (OCCI) model with respect to the OCCI standard specifications, (ii) the first unified system which combines the functionalities of the worldwide cloud providers: Amazon Web Services (AWS), Microsoft Azure and Google Cloud Platform (GCP), and (iii) allows a dynamic configuration at runtime during the execution of the application. MODEMO permits to timely adapt resource capacity according to the workload intensity and increase application performance without introducing a significant overhead.