I’ve been Reading Robert Letham’s The Holy Trinity over the past few days.  Heck, Nick says that if he could only save one of his books from being burned (besides the Bible) this is the book he would save.  So I thought I probably at least ought to read it.  So far it seems like a fine book, but certainly not at the book-I-would-save-above-all-others status.  One aspect of the orthodox doctrine of the Trinity confuses me as I dig deeper.  In his section on Gregory of Nyssa, Letham writes,

Because of his focus on the three, it is not surprising that Gregory was accused of tritheism.  He felt obliged to defend himself against the slur in his short but intriguing work On “Not Three Gods”to Ablabius… Gregory responds to Ablabius’s suggestion that the Trinity is comparable to three men sharing a common human nature.  This analogy follows the generic definition of ousia and hypostasis that Basil propounded and Gregory himself accepted.  The problems are obvious.  There are a vast number of men, but only three and ever three persons of the Trinity — no more, no less.  (pp. 156-7)

I am having trouble understanding why holding to a biblical theology limits us to only three persons.  I see the proposition routinely asserted but so far I have been unable to find an argument for it.  I have no desire to deny this proposition but I am at a loss to know how to defend it.  In fact, it seems to rest on similar logic to that used by those who accepted the authority of the Hebrew Bible but not of the New Testament: God says He is one; therefore He cannot be three.  So Christians argue that the New Testament leads us to understand God as three persons; therefore God cannot be more than three persons.

Can someone point me to some passages in the the Church Fathers that make the argument explicitly?  Or at least can you give me some arguments to defend the proposition?