Have multiple trees in one table using CakePHP Tree Behavior

I'm converting a flat list into a tree in my CakePHP app and found that there is an existing behavior that has this functionality. My table is not one giant tree, but consists of many user-generated trees: basically, each user can create their own folder structure. However it seems that the Tree Behavior would only keep track of lft/rght values across the entire table as if it is one giant tree. Hence if a new folder or sub-folder is added, the entire table needs to be updated.

Am I wrong about how the Tree Behavior actually works or if not, is there a way around this?

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