Not with just "any network analyzer", like the 8711; you need a 4 port network analyzer, such at the Agilent E5071C with 4 port option. Isn't there a process (perhaps tedious and manual) to do this
An affordable solution is the VNWA. Its only a 2-port VNA, but its application includes calculations for 3-port measurements. As I recall, DG8SAQ included that specifically for baluns. Users say it