A technique protects against failure of a network element using Multi-Topology Repair Routing (MTRR) in a computer network. According to the novel technique, a protecting node (e.g., a router) maintains Multi-Topology Routing (MTR) databases for a first topology and at least a second topology. The protecting node determines whether any acceptable repair paths are available in the first topology for a protected network element (e.g., node, link, etc.) of the first topology. If not, the protecting node may establish a repair path (e.g., for Fast ReRoute, FRR) in the second topology for the protected network element.