What is the Biblical basis for the doctrine of the Trinity consisting of different persons?

In [What is the Biblical basis for the doctrine of the Trinity?](https://christianity.stackexchange.com/q/72/27036) we have explored the biblical basis for the doctrine that the Father is God, the Son is God, and the Holy Spirit is God. However, what is the Biblical basis for the doctrine that: 1. the Father and the Son are different persons; 2. the Son and the Holy Spirit are different persons; and 3. the Holy Spirit and the Father are different persons? In [this answer](https://christianity.stackexchange.com/a/2049/27036) , my question is addressed but not answered; other answers also attempt to explain how the three persons are one, instead of how the three persons are distinct.