This paper proposes Steiner-based algorithms to extend already deployed tenant slices or Virtualized Network Functions Forwarding Graphs (or Service Function Chains) as demand grows or additional services are appended to prior service functions and chains. The tenant slices are hosted by Network Function Virtualization Infrastructure (NVFI) providers that can make use of the proposed algorithms to extend tenant slices on demand for growing traffic loads and service extensions including protection and security services(such as extending a slice with a dedicated security slice). The paper proposes a Steiner-based ILP as an exact solution for small graphs and Steiner based approximation algorithms to improve scalability for larger problems.