I am going to be editing this post, but I wanted to go ahead and submit it to my blog. It has been my contention that without the doctrine of divine simplicity being presupposed, the Trinity doctrine falls. Conversely, other Trinitarians have argued that it is difficult to make sense of the Trinity doctrine if one presupposes or believes in a simple or non-mereological deity. But it seems to me that without the presupposition or belief that God is simple while also being three persons in one God (one divine substance), what one has with the doctrine of God's triunity is really tritheism or modalism (depending on the respective formulation of the dogma). In any event, a number of thinkers have taken issue with the simplicity doctrine. One of these individuals is Dr. Alexander R. Pruss. You can reference his entire discussion at http://www9.georgetown.edu/faculty/ap85/papers/On3ProblemsOfDivineSimplicity.html
Pruss' first objection to the divine simplicity doctrine is that it does not seem to allow for a meaningful predication of those attributes which distinctly characterize God. Let A = "God's perfect justice" and B = "God's perfect mercy." If the divine simplicity doctrine is correct, then A is ontologically identical with B such that it appears that it is not meaningful to discourse about God's perfect justice or perfect mercy since the two attributes would be identical in this case.