How does adding a second subwoofer improve your systems SQ?

Toole didn't throw up his hands in defeat to him the answer was in equalization. I also agree with his assessment that to much absorption leads to an acoustical dead room like a studio, reflections aren't all bad and the lower 300-500 hz is where most problems are unless your speakers are all over the place in the upper area. Multi sub is easier to get the bass equalized  but for a single position and enough work one can suffice. 

Toole is so great. I especially liked him in Becket. 🤴 

After watching the video posted by @audiokinesis I have to say this mirrors my findings. I have gone down the road with numerous acoustic panels, bass traps, and diffusers. I would say the best I tried were from a long defunct company called Eighth Nerve, and the most effective trap was the triangle placed in the ceiling corners. In my system my DIY DBA made the most significant difference (in a bi-amp or tri-amp set up) and I was able to rid myself of a lot of extra stuff hanging on my walls in the process.

Atmasphere, in general I agree with what you say with point source speakers that are not digitally corrected and time alligned. However when it comes to linear arrays particularly tall ESL dipoles the situation changes somewhat. If the subwoofer system does not want to get loss under the linear array it also has to radiate like a linear array. This requires a driver every 5 feet or so with the line ending at wall boundaries. If the system were on a long wall this might require more than four units. Dipole ESLs just do not do well under 100 Hz. As you mentioned crossing up higher than 80 Hz without digital correction won't work well. You will always know there is a sub woofer down there. But with time and phase alignment you can go up higher. I cross at 125Hz 4th order and unless you open your eyes you would never know there was a separate subwoofer system and because the sub woofers are forming a linear array the relative volume between the subs and satellites does not change with distance. The linear array also minimizes room effects which allows me to do room correction with much less power. The the resulting improvement in performance of the ESLs at volume is imminently noticeable as is the marked improvement in head room. It's like adding a turbocharger to your engine. 

Mike  

I should also note that I have never used digital correction with a point source system. I have to believe that subwoofer integration would be easier and better. Although I thick you could get away with a higher crossover the benefit would be questionable as the woofer in the satellite has a very limited range whereas with a one way ESL the entire frequency band is affected by the long excursions bass requires particularly at volume. When a very low note comes along say 18 Hz at volume you can actually hear the music flutter.