The service delivery model of cloud computing acts as a key enabler for big data analytics applications enhancing productivity, efficiency and reducing costs. The ever increasing flood of data generated from smart phones and sensors such as RFID readers, traffic cams etc require innovative provisioning and QoS monitoring approaches to continuously support big data analytics. To provide essential information for effective and efficient bid data analytics application QoS monitoring, in this paper we propose and develop CLAMS-Cross-Layer Multi-Cloud Application Monitoring-as-a-Service Framework. The proposed framework: (a) performs multi-cloud monitoring, and (b) addresses the issue of cross-layer monitoring of applications. We implement and demonstrate CLAMS functions on real-world multi-cloud platforms such as Amazon and Azure.