A multi-mode circuit implements the functionality of a limited number of circuits, called modes, of which at any given time only one needs to be realised. Using run-time reconfiguration (RTR) of an FPGA, all the modes can be time-multiplexed on the same reconfigurable region, requiring only an area that can contain the biggest mode. Typically, conventional run-time reconfiguration techniques generate a configuration of the reconfigurable region for every mode separately. This results in configurations that are bit-wise very different. Thus, in this case, many bits need to be changed in the configuration memory to switch between modes, leading to long reconfiguration times. In this paper we present a novel tool flow that retains the placement of the conventional RTR flow, but uses TRoute, a reconfiguration-aware connection router, to implement the connections of all modes simultaneously. TRoute stimulates the sharing of routing resources between connections of different modes. This results in a significant increase in the similarity between the routing configurations of the modes. In the experimental results it is shown that the number of routing configuration bits that needs to be rewritten is reduced with a factor between 2 and 4 compared to conventional techniques.