Definitely this splitting a tree is one of the features I could really use. You start with one file and later on you realize it is getting too big (due to FTM performance limitations, number of names/families, .....) and you want to split it up. In my case I would like to take my tree and break it into 4 trees, one for each grandparent. Obviously the lower level would be common and I can live with dup trees in this case as that is easy to maintain. Unfortunately there is not an easy way to do this with my trees which are truly hour glass trees where I cannot start at the lowest descendent or highest ancestor as I miss siblings, in-laws, ... The export option using the Ancestor filter tries but does not provide enough options and the only way I know to do this is copy my tree and then start deleting branches and hope there is no crossover. This would be a top 10 feature for me.
As for the common part of the tree another option would be to provide a "reference" feature that could refer to another tree at a certain point, this way you would not have to have multiple copies of the same data.