I’m almost 39; read it’s “extremely rare” to grow inches taller @ my age but docs didn’t say impossible. What rare conditions or other would cause it?

It is impossible. The closest condition known to cause this is acromegaly, which affects about 1 out of 17,000 people.
This is due to overproduction of growth hormone, usually from a benign pituitary tumor, but even with acromegaly, while the hands and feet, ears and nose may grow, because the growth plates have closed even those with acromegaly will not grow taller.
Impossible. Doctors say it is impossible. Growth hormone cannot make a person grow taller unless there are growth plates in the long bones that are still active, as in children and teens. In real life, height growth does not happen at age 39 years. Only in the internet world, might there be stories of middle-aged adults who have finished growing but later resume growing in height.