It'd have to be something that gives you a reason to use FF over Chrome or Safari or IE/Edge. A social approach has "virality" to it. "Oh we're all posting on this Tweet in FF-Social, that's why you're not seeing the replies. Go get FF and join in. Here's the invite link for our group."
Some add-ons and (earlier) wrapper sites tried similar things, but I think FF is one of the few companies that might have wanted to try this, had (at one time) the critical mass & goodwill to pull it off, and had the right vehicle for it.