Real-time virtualization is an emerging technology for embedded systems integration and latency-sensitive cloud applications. Earlier real-time virtualization platforms require offline configuration of the scheduling parameters of virtual machines (VMs) based on their worst-case workloads, but this static approach results in pessimistic resource allocation when the workloads in the VMs change dynamically. Here, we present Multi-Mode-Xen (M2-Xen), a real-time virtualization platform for dynamic real-time systems where VMs can operate in modes with different CPU resource requirements at run-time. M2-Xen has three salient capabilities: (1) dynamic allocation of CPU resources among VMs in response to their mode changes, (2) overload avoidance at both the VM and host levels during mode transitions, and (3) fast mode transitions between different modes. M2-Xen has been implemented within Xen 4.8 using the real-time deferrable server (RTDS) scheduler. Experimental results show that M2-Xen maintains real-time performance in different modes, avoids overload during mode changes, and performs fast mode transitions.