How does room correction treat multiple passive subwoofers?

You're smart. That is a question you should ask. HOW? The correction is as good as the programming and the programming has parameters. It can't tune 4 separate subs from one mic reading. Nor can it tune 4 separate subs on one common amp output. BTW a servo sub is only as good as it's programmer is too. Zero reaction time is the key to all correction.

The better way is to tune the room mechanically first. I use a mic and SPLs via Helmholtz and proper room acoustics. Then worry about DSP. You won't need it though. A simple GEQ or PEQ will work much better. I use correction, sometimes and servo subs all the time.

There is something about DSP that sucks the life out of certain music. I have to tune by ear for that last little bit. DSP works better in a car or really weird rooms.

Personally, I think the answer is "poorly." However, the Distributed Bass Array fanboys have other ideas.  Feel free to go research it.

Since I don't ascribe to that religion however I'd encourage you to use active subs with EQ.  For more information on the benefits and configurations needed please read this paper:

https://www.minidsp.com/applications/subwoofer-tuning/tuning-multiple-subs

Since I don't ascribe to that religion

@erik_squires 

Its not a religion- its based on physics.

At 80Hz the waveform is 14 feet long; it takes 2-3 iterations before the ear can know its there and its frequency. By that time the waveform has bounced around the room a bit, so is entirely reverberant as well as any frequencies below that (and likely some above as well).

That is why a mono signal can be used for bass; its the harmonics of the bass note coming from the main speakers that tell you where the instrument is. The only tricky bit is making sure the sub has no output above 80Hz else it can attract attention to itself.

If the room has parallel walls front and rear a standing wave will exist. The  reflection from the wall behind you can cancel the incoming wave, causing a very noticeable and measurable loss of bass at that and nearby frequencies. If this occurs no amount of DSP can correct it, since its caused by cancellation; you could put all your amplifier power into that and it will still cancel. DSP is not a solution and neither are bass traps as they are too ineffective and can't be tuned to the correct frequency needed; different in any room.

But a DBA can break up the standing waves quite effectively. At that point the DSP can do its job correctly, and amplifier power is not gobbled up. So the correct answer to

How does room correction treat multiple passive subwoofers?

is 'quite well!'

Its just physics. I am curious- why do you resist this? I mean beyond being mistreated by another member (apparently now banned), who must not be named?

@blue_collar_audio_guy 

Let’s answer this question first: will it treat it as one sub?  Yes.  When done right, you will hear the array as a single source. @erik_squires is correct that you would be better off using powered subs. DBA has been studied by some credible people in the industry, including Dr. Floyd Toole, Dr. Earl Geddes and Dr. Sean Olive. @helmholtzsoul is also correct when he said the software is as good as the programmer. This is true of all software, right?  The reason some software misses the mark is because when dealing with frequencies between 20HZ and 300HZ you have to address not only frequency domain issues but also time domain and phase domain issues. It gets complicated fast. And that’s why a computer will do a better job than us. DSPEAKER has some very easy to use gears that can do a great job.  All that will be left to do is add some acoustic help (corner traps etc..) and do a final touch up by ears to set it to your liking. According to Toole, when you get the bass right, you already get 30% of your system right. DBA is the easiest and cheapest way to achieve it. Good luck.