Yes and no; in practive, yes, Philosophy usually branches off, as really it's jsut thought on something, ie, "Philosophy of Ethics" is thinking about how to treat one another, "Philosophy of Religion" is considering of God is alive or Dead or a Delusion, "Political Philosophy" is thinking of the very best ways to screw your populace over... ;)
So yes, it branches off, but like the branches of a tree, they all need to coalesce and come together somewhere, at the middle-point of the tree, the bark, that over-grown stem, so to speak, hence the concept that our thoughts are all "stemming" from somewhere...
So philosophy deals in many fields, but ultimately meets in one place or, at the very least, is categorized under the umbrella of thought and thinking.