A multi-tenant software as a service (SaaS) provider has to meet the needs of several tenants which adopt its services with diverse business requirements. The tenant needs vary widely with time, and the provider has to account for such fluctuations by suitable provisioning at its end. Handling this elasticity arising out of the tenant base is one of the key challenges for the SaaS provider. In this paper, we study the problem specifically in the SaaS context with the idea built around license provisioning in a tenant–provider perspective. For a given set of tenants with diverse license requirements, it is important to analyze whether there is any way to on-board them such that all constraints laid out as part of the service-level agreement can be honored. The total number of licenses available with the provider plays a crucial role in answering this question. We propose an intuitive model of elasticity that can capture anticipated license need variations at the tenant end. We propose an ILP-based approach for solving this schedulability problem for a collection of tenants. We also propose a simple-minded greedy heuristic to solve the on-boarding problem with elasticity constraints. Results show that our approach gives acceptable performance.