I figured out the problem.
First, I had opened a ticket with GoDaddy ProSupport. They told me:
Since it was built using a multisite WordPress structure, I’m afraid that we are unable to work on it because of the liability of making changes that can affect other websites using the same database. We recommend hiring a specialized developer to handle work on this website.
We do have a support article which offers some general advice on setting up multisite environments, but things like this are a bit out of our scope of support. You can check out the article here: https://www.godaddy.com/resources/skills/wordpress-multisite.
It turns out, my MultiSite WAS setup properly. However, when you have this kind of structure that I (the OP) asked about, it’s setup with the following “Add on Domain”
A.com ('parent' site, multisite enabled) IP: 1.2.3.4
/home/public_html
someothersite.org (subsite, edited URL)
B.com ('parent' site, multisite enabled) IP: 1.2.3.4
/home/public_html/b.com
AThirdsite.org
So what you have to do is to go cPanel admin, then go to “Addon Domains” and register athirdsite.org as an addon domain to b.com. Then – very important – make sure to override the Document Root to point to /home/public_html/b.com
Note that when you used cPanel to create b.com, it added the “Addon Domain” for you automatically. For the subsites, you have to do this manually, because you create them via WordPress’s sites menu, not via cPanel, so it doesn’t know about the second multisite.
IMPLICATION:
I think this means that b.com could never have dynamically assigned sites, but it may be possible to jigger this with the right domains and wildcards.
Note that A.com could have dynamically assigned sites, as any domain that hits the IP address for your Hosting account will automatically go to the default domain.