We present a new system architecture that extends Multi-Topology Routing to build several virtual topologies on top of existing (real) ones. The main goal is to reduce the protocol overhead that may occur with a large number of topologies and to accommodate a large set of demands with heterogeneous QoS requirements. Instead of designing link weights for different topologies, our system derives virtual topologies from real ones (e.g., cost, latency) using Lagrangian relaxation. In this case, only Lagrangian multipliers are communicated by the network management system to routers, one per real topology which drastically reduces overhead. In addition the virtual topologies that are created are "silent", i.e., they do not exchange additional LSA messages.