MultiDLO is a real-time algorithm for estimating the shapes of multiple, intertwining deformable linear objects (DLOs) from RGB-D image sequences. Unlike prior methods that track only a single DLO, MultiDLO simultaneously handles several objects. It uses the geodesic distance in the Global-Local Topology Preservation algorithm to define both inter-object identity and intra-object topology, ensuring entangled DLOs remain distinct with accurate local geometry. The MultiDLO algorithm is demonstrated on two challenging scenarios involving three entangling ropes, and the implementation is open-source and available for the community.