It is clear from the March 31st press release on Moose, Sheep, and Goat Controlled hunts that one may not apply for a controlled hunt for another species, with exceptions. However, if I were to apply for a deer controlled hunt, may I still apply for an elk or pronghorn controlled hunt? Please also let me know how likely it is (based on previous years data and your best guess) that there will be leftover nonresident general season tags available for deer and elk.
You can still apply for more than one species during the May 1-June 5 application period so yes, you can apply for deer and elk and pronghorn in the same year if you want to.
Going by previous year's sales, it is most likely that there will be some nonresident deer and elk tags available for sale to hunters for use as a second tag in August. Some capped elk zones might not be available then, elk tags for most of the state will be available.