Stack Exchange supports its communities in a number of ways. They periodically give branded swag to high rep users. They make donations on behalf of moderators to charities/causes during the holiday season. They also, at least for TeX.SE, have corporate membership in a relevant society.
I think there may be a relevant society that Stack Exchange might join that would help promote our site and provide benefits to out members. Should we ask Stack Exchange for such support, and if so where?
Some, likely not very good, ideas are:
National Postdoctoral Association