Modern communication networks face significant challenges due to the constant growth of traffic volumes and the need to effectively manage network resources. Standard routing protocols based on finding a single shortest path can lead to uneven load distribution and limit the overall throughput. One of the promising approaches to solving these problems is multi-path routing, which allows the use of multiple available paths for data transmission. In this paper, we propose a modification of the Dijkstra’s algorithm that extends the classical approach to find a set of optimal routes in a single algorithm run. The developed modification allows forming not only the main tree of shortest paths, but also additional trees of alternative routes, saving them based on certain conditions.