Thanks for the link @UWfromCA .
According to the Foster school description:www.washington.edu/students/gencat/academic/school_business.html#UNDER
Double Baccalaureate and Second Baccalaureate
Students who wish to earn more than one baccalaureate degree should consult an academic adviser in the Foster School Undergraduate Program Office, either during or before their junior year. Persons seeking a second baccalaureate should apply at the University’s Office of Undergraduate Admissions. To be considered, applicants must complete by quarter of entry the same prerequisites for admission as applicants for the first baccalaureate degree. Since the number of eligible applicants exceeds available space, acceptance is competitive, based on the criteria listed above for selection of first baccalaureate degree applicants. The Foster School uses the GPA for the last 90 credits earned.
So, basically finish GE and apply before Junior year as other regular applications. Definitely need to talk to the Foster academic adviser to see what they recommend.