It is a beautiful tree. As others have mentioned, since there has been so much that has been removed, the tree is currently in a very weak stage. You will really need to watch the tree. It may not be taking in as much water, so you may have to adjust accordingly. However, you might want to mist or lightly hose off the foliage to keep the humidity up. Also, maybe protect the tree from intense afternoon sun.
I am concerned about this tree because one minor scale, mite or fungus problem could wipe this tree out in a matter of a week. However, I would not spray any chemicals on it unless it becomes necessary.
Rob