How does adding a second subwoofer improve your systems SQ?

Avanti,
Having two subs is a great advantage to achieving a balanced sound if you have limited room to position them.    

This is what I was waiting for. Unless you have a dedicated audio room, I don't, there are definite limitations to most all rooms. My system is in my living room. I simply can't put subwoofers where they might sound best. I'm confined to placing my sub next to one of my main speakers. Avanti, so your thesis is, buy a second sub and place next to the other speaker and enjoy the music. 

I am a huge fan of Floyd Toole, but in general he seems to not consider affordable bass traps as solutions. He kind of alludes to this:

Short of hiring an acoustical consultant, and being willing to rearrange the furniture and possibly rebuild the walls, what can be done?

So his entire solution space is outside of this possibility, which may be a choice based on who they expect their customers to be.

Other, more modern acousticians have written with the presumption that bass traps are an option and they don’t throw up their hands quite as easily to the problem.

Once we allow for bass traps, things get much better for subs and EQs, and it is from this perspective that I often challenge the DBA cultists. A well integrated single sub, in a well treated room, including bass traps performs really amazingly well.  Two subs is better.

Best,
E

My four subs are in my living room and only one is visible.They easily tuck behind furniture,the wiring runs along the baseboards.The one that's visible is going to masquerade as a table supporting a plant soon,when it's safe to shop again.
Yes Erik there are room treatments too;-)

simple answer

1.  2 subs load the room better, in many applications

2.  bass is supposedly non directional, but in reality, subs have crossovers that 'leak' into higher, directional frequencies... stereo subs put these in L&R space where they belong (moreso)

markj941 OP

If members here that are pro one sub, and running it off a HT sub output.
Forget that single HT preamp sub output, get two subs run both subs from the main L & R preamp outputs 
You will find if you have two subs and in the HT programming "set the mains for large" with "no sub" picked, then cross the 2 subs in at where your mains fall off, get the phasing and level right ect.
Your in for a treat from what can come from active proper stereo setup bass bins.
Your mid sized floor standers or large book shelves will have the scale of sound that you only get from big floor standers like Wilson Alexia Max Alex ect.

Cheers George