GI Bill STEM Extension Act of 2017 This bill directs the Department of Veterans Affairs to pay the lesser of nine months or $30,000 of additional Post-9/11 educational assistance to selected eligible veterans who have used all of the Post-9/11 educational assistance to which they were entitled and who: (1) are enrolled in a postsecondary education program that requires more than the standard 128 semester (or 192 quarter) credit hours for completion in a specified science, technology, engineering, or mathematics (STEM) field; or (2) have earned a postsecondary degree in one of those fields and are enrolled in a teaching certification program. In selecting eligible individuals, priority shall be given to individuals who: (1) require the most credit hours; or (2) served on active duty service for at least 36 months with an honorable discharge, continued active duty service after such 36-month period, or served at least 30 days of continuous active duty service with a service-connected discharge. Such additional assistance may not be transferred. The maximum amount of assistance paid to all eligible individuals in a fiscal year may not exceed $100 million.