We actually considered reaching out to PF early in the site's development, but we got shut down by their moderators. Their opinion appears to be that any mention of a competing site constitutes an advertisement, which is against the rules there. If we could think of some way to create a partnership that they would actually be interested in, I'd certainly love to see that happen, but we haven't had any ideas that seem promising. Even so, I do occasionally send people over to PF when they have particularly discussion-y questions.
Physics Forums does have a chat room of some sort (I've never participated), but they only open it up for a few hours at a time every few weeks because of the stress it puts on their server.
EDIT: I've been thinking of a couple of things we could possibly offer Physics Forums:
- As in my comment, every once in a while I'll see someone asking a question on PF which is addressed quite well by a question on Physics.SE. In those cases it would be great to be able to post a link to the relevant PSE question in the PF thread.
- PF occasionally gets people who, though not trained physics researchers, have ideas they are interested in publishing and are looking for feedback on the work. (example) Ever since their Independent Research subforum was shut down, there is no appropriate place on their site for those kinds of discussions, but some of them can be accommodated here. In particular, either this site or theoreticalphysics.SE could accept questions about what prior research has been done in a particular field, and our chat room could be a good place for people who are legitimately interested in getting feedback about their ideas.
- The General Discussion forum gets a number of non-physics-related questions that are (or could be) addressed by other Stack Exchange sites. (example, would be great for money.SE) Once people at PF are aware of the Stack Exchange network through this site, they might also be interested in making use of other SE sites.
I'm making this community wiki so that other people can add items to the list as they think of them.