Algorithm to detect best path in a multigraph

Question

essentially I have a multigraph where each edge has its own identity and the weight of each edge is dependent upon some starting input. I have created a dijkstra-based search algorithm that can detect the shortest path from start to destination, however for my use case the most optimal path may actually be multiple paths. For example, if my starting input is 1000, the weights are calculated and assigned and will return the shortest route. but it may be more efficient to split the starting input among several routes. I have a multigraph[[0,2,2,2],[2,0,0,1],[2,0,0,2],[2,1,2,0]] where the numbers represent the number of edges connecting nodes ABCD. the most efficent route from a to b might be to send 500 along one of the edges connecting A to B and 500 along the other edge, or even to send 500 from A to D then to B etc depending on the starting input. is there any resources describing algorithms that might help?