Art gallery variants with pairwise visibility?
I'm not aware of any such work.  However, I would expect that such a problem would be NP-complete and, for polygons with holes, would be as hard to approximate as Set Cover.  The relatively straightforward vertex/vertex guarding problem, in which guards can only lie on vertices and only vertices need to be guarded, is this hard (Eidenbenz, Stamm, and Widmayer (2001)).

For simple polygons, I expect such a problem would be:


NP-complete
APX-hard
Approximable to within a factor of $O(\log(\rm{opt}))$, where opt is the optimum number of guards.


The vertex/vertex guarding problem is APX-hard for simple polygons (Eidenbenz (1998)).

The best algorithms for the art gallery problem for simple polygons are based on building small $\varepsilon$-nets.  In simple polygons, the range spaces induced by visibility polygons have constant VC-dimension.  Circles do as well.  Therefore a range space induced by visibility polygons in a simple polygon, circles, and the intersections and unions thereof, will also have constant VC-dimension and you can get a $O(\log(\rm{opt}))$-approximation algorithm.

I thought about this problem a little for my thesis, but came to the opinion that there weren't any particularly interesting variants that didn't seem to reduce fairly closely to a known problem involving single-guarding.