Can we add more vertices to a tile in a Tileset?

Godot Version

4.2.1

Question

Hi! I am new to shaders, and I was trying to make a tree sway. I was able to make it sway. Next, I made a tile set with a tile that has the shader material that makes it sway. But I wanted the tree to sway only a part of it and the rest should be static, (I attached an image) my problem is, that I don’t know how to do it because the tile only has 4 vertices. Is there a way to make it 6 vertices?

I made a Polygon2D, and I was able to make it sway the way I wanted to. I was also thinking about adding that Polygon2D in a Scene Collection to use it as a Tile, but I don’t know the performance implications of doing it.