Cyber-Physical Systems are ever-increasing in complexity and new methods and tools for developing them are needed. To support these highly dynamic systems, increasing the flexibility of the modeling languages is desirable. This paper proposes and examines a Modelica language extension to support dynamic overconstrained graphs with reconfiguration at runtime. Two applications of this new feature are also discussed: synchronous AC power systems and incompressible fluid networks. Reported findings suggest that supporting dynamic overconstrained graphs might yield performance benefits and provide the possibility of simulating systems that can not currently be simulated in existing Modelica tools.