I have a portion of my deck that's a 4' square connecting stairs that go up and down from it. One of the corner posts (green post in the pic) has sunk between 1/2 and 1 inch and I'd like to raise it and pour a new deck piling to stabilize it. I don't think it's still sinking and has been stable in its current position for at least a few years. The wood seems all in good shape.
I'm a total newbie at this and am evaluating whether to even try this myself. I thought about using a jack to raise the corner, but I don't know where I can place the jack such that it won't interfere with my ability to dig the hole for the new concrete. When I tried to place it anywhere a foot or more from the post, it basically tries to lift the entire platform rather than the corner I'm concerned about. How could I effectively and safely raise the deck here while still leaving enough space to dig a hole around the offending post? Or is there another technique that might be better?
Approximate design below. Posts are 4x4 and platform is 4' x 4'.
To respond to @Ecnerwal's question about the screws versus nails attaching the framing to the post: lots and lots of nails, sunk deep into the wood.