There are so many climbers on Mt. Everest today that there is now a helicopter rescue service there. They operate rescue up to 21,000 + ft. Because this is essentially stationary service it seems that engine modifications like a larger compressor section would be warranted.
In stories on the internet regarding these helicopters, none mention engines.
My employer had two Rolls-Royce RB211s operating at about 7,000 ft as stationary power and the power rating was cut in half for the altitude, so operation at 21,000 ft is impressive.