This document proposes a novel video caching framework that uses MPEG-4 Fine-Grained Scalable (FGS) video with post-encoding rate control to achieve low-cost and fine-grained rate adaptation. The framework allows clients to have heterogeneous bandwidths and enables adaptive control of backbone bandwidth consumption. It examines issues in caching FGS videos, such as determining the optimal portion to cache (in terms of length and rate) and optimal streaming rate to clients. Simulation results show it significantly reduces transmission costs compared to non-adaptive caching while providing flexible utility to heterogeneous clients with low computational overhead.