Often people have lamented the "this is appropriate on multiple sites, but people yell if I post copies of it on both" or "I'd post it on the other site, but it doesn't get enough eyeballs - this one gets more (even though its off topic here)". This is a problem.
The answer to this problem would be to get the eyeballs from here to there. Some chatrooms do this. For example, the photography chat room has Software Recommendations photography tag as part of its feed and gardening chat room has the gardening tag from Sustainability. There are other examples out there too.
And while this helps the active members of chat get to other sites, the active members of chat are often a small minority of the site as a whole and don't constitute that many eyeballs.
So, on the right hand side of the main page/questions side of the site, have a 'recent questions on other sites' that consumes the feed for a specific tag on the other site. So that the photography main page will see the questions tagged as photography on software recommendations... and maybe they'll want the lenses tag from physics.SE too. And likewise, gardening and sustainability can cross promote each other's site. And AskUbuntu can take note of the ubuntu tag on unix.SE and so forth. There are lots of cross site possibilities.
A key point to consider is that the more involvement with stack exchanges as a whole, the more likely that a person is likely to remain on stack exchange and contribute (a good thing). Furthermore, having this cross site tags of interest may help avoid verbatim cross posts (a bad thing) and at the same time provide new users with "oh, there's a stack exchange for that over there too?" when considering where to ask questions - because they see it on the front page.
This list of cross site tags of interest would be maintained by the mods on the site.