Shortest Path

How can we use Dijkstra's or Bellman–Ford's algorithm to find shortest path in a graph whose some of edges are affected if we go specific vertices. Such that, the affected edge's length will be more than or less than the original length.
By generating extra nodes for every variation of the graph, but that's just some wild assumption.
Actually I thought of what you said before, but when I calculated my variations, i found more than 10^4 * 4^10000. So it will be very very unefficient.
I think no one knows a solution?
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