STEM Opportunities Act of 2016 This bill directs the Office of Science and Technology Policy to establish a STEM Inclusion Interagency Working Group which shall focus on the creation of a more diverse and inclusive STEM (science, technology, engineering, and mathematics) workforce. The National Science Foundation (NSF) shall strengthen the goals and activities of the ADVANCE (Increasing the Participation and Advancement of Women in Academic Science and Engineering Careers) program to focus on increasing the recruitment, retention, and success of all women in STEM, including minorities and persons with disabilities. The NSF shall: award a grant for the establishment of at least one Center for Excellence for Inclusion in STEM; collect institution-level data on the demographics of STEM faculty at different types of institutions of higher education; award grants to institutions of higher education (or their consortia) to implement or expand evidence-based reforms for recruiting, retaining, and advancing students, fellows, trainees, and faculty from underrepresented groups in STEM; and administer three specified Presidential Awards for Excellence in Science, Mathematics, and Engineering Mentoring to recognize annually outstanding mentoring in STEM fields in primary, secondary, and higher education.