An Odd Question

Sonic impact of having multiple (3) acoustic guitars on stands in your listening room?

To kill off most sympathetic resonances
Put a soft clamp across all the strings, and block off the sound hole in the bodies.

Cheers George

Yes there are sympathetic resonance issues, but unless you can actually hear them it's not an issue.  BTW, every object in your listening room is subject to sympathetic resonance. 

moving things around in listening room is a great tweak, sometimes surprising changes...

I would imagine they would act like Helmholtz resonators.  I have heard and believe a story of Klipschorn cabinets being used as effective bass traps.

Possible effect I believe would be to pull out those frequencies, but generally, I believe and stand to be corrected, the small mouth openings would minimize this effect.

Why not ask guitarsam, he knows everything