19 pages, no figures.We explore cosmology of intersecting braneworlds with induced gravity on the branes. We find the cosmological equations that control the evolution of a moving codimension one brane and a codimension two brane that sits at the intersection. We study the Friedmann equation at the intersection, finding new contributions from the six dimensional bulk. These higher dimensional contributions allow us to find new examples of self-accelerating configurations for the codimension two brane at the intersection and we discuss their features.OC is partly supported by a Marco Polo fellowship of the University of Bologna. KK is supported by STFC. GT is supported by MEC and FEDER under grant FPA2006-05485, by CAM under grant HEPHACOS P-ESP-00346, and by the UniverseNet network (MRTN-CT-2006-035863).Peer reviewed