What is the Biblical evidence that there are ONLY three persons in the "Trinity"? (This is a followup to the various answers for the question What is the Biblical basis for the doctrine of the Trinity?)

The specific concept of 'trinity' isn't specifically spelled out in the Bible.  Instead, we have deduced from various scripture verses that there are three distinct persons within the Godhead.

What is the Biblical evidence that there are only three persons in the Godhead?  Why don't trinitarians believe that there could be others that are not revealed specifically through scripture, or that we can attribute multiple "persons" to a single concept of Father or Holy Spirit?
Our biggest clue is from this scripture:

Matthew 28:19 (NIV)


  Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,


Beyond that, I know of no other verses that limit the Godhead to three persons.