Can I turn a 4 X 4 deck post, eight feet high, into a 6 x 6 post by laminating a 2 X 6 and 2 X 4 to it?
If I understand your description correctly, you have a maximal load area of ~38 ft². If so, 4x4s are more than sufficient for the posts. (Check your trusted load tables; don't believe some random guy on the Internet.) If you replace some posts there is no harm in upgrading them to 6x6s, but I don't see a reason to sister onto the existing 4x4s.

However, it sounds like there is so much rot that it will be easier to tear down the entire deck and build a new one. If you do that, the new deck will of course need to meet current code requirements.