Turn based multiple agent sizes

Hello. I am working on a turn based game with multiple unit sizes. I can block large units fine but the unit that I use its travel provider gets only one node blocked. In the photo there are two large (2x2) units. The one that is moving has one node blocked. When it moves it can go into smaller units space and smaller unit get stuck. Is there a way to make moving unit have a bigger size?(Clearance path algorithm)

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I found a half way solution to this. I check if the 2x2 tiles are empty first. There is clearance based A* algorithm. Wouldn’t it be a more elegant solution here? Because large units can still pass through 1x1 spaces.

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Bump. Is there a solution to this?