Anecdotal sources suggest that if you use the "popcorn" button on your microwave at a high altitude area, it will still pop, you just have to wait for a few more seconds.
When in high altitude areas, microwave cooking times may need to be adjusted. But high altitude instructions are usually applied to those recipes that involve liquids.
As altitude increases and atmospheric pressure decreases, the boiling point of water decreases. As per USDA, to compensate for the lower boiling point of water, the cooking time must be increased. Turning up the heat will not help cook food faster.
No matter how high the cooking temperature, water cannot exceed its own boiling point — unless if using a pressure cooker. Even if the heat is turned up, the water will simply boil away faster and whatever you are cooking will dry out faster.
Learn more about high altitude and its effect on cooking at Thermoworks.com.