Yes, you certainly can. I currently run four stabilizing chambers and I made a manifold that allows me to run all four at the same time from one vacuum pump, if I desire to run all four at once. (So far I've only run three at once, but will probably have all four hooked up at the same time in the near future.)
Found a picture from right after I first put it together. Quick connects for connecting lines to the chambers. On the far right is where the line runs to the vacuum pump, plus a release valve to release vacuum. Each connection also has a valve to be used as needed or to close off the line when not in use or to help facilitate adding or removing a chamber from vacuum while not releasing vacuum from the other chambers.
Yes, I love playing with color when stabilizing blanks! Having more than one chamber, I can do more with different colors at one time. Though my largest chamber - 6" ID x 24" tall - is dedicated just to clear work.
That's a nice set up. And the blanks are nice as well.
I've watched the How-to videos, and saw that you have to pay attention to the bubbling when starting it up. I didn't know how multi tanks would work out. That is, if the bubbles rise at the same level. OR not.
I will admit - watching the level of bubbles does get tricky when you have more than one chamber you're trying to watch - but if I can keep the wife and kids from coming in the shop during that 10 minute or so time, I can do just fine!