After reasonable trawling of your user guides / vids and here on the forum it seems the only reference to compatible cart systems is Virtuemart.

Is this the case? Are there other cart modules that will work?

NO.
You can install an use different eCommerce application.
See the list of extension that are currently defined in the JMS tool menu.
www.jms2win.com/en/list-of-extensions?vi...id=269&Itemid=53

Perhaps you make a confusion with the "Bridge for VirtueMart" that we have created to process the billable website creation from the front-end.
This is just a particular case where we propose to use VirtueMart to manage the order of website creation and the payment.

For your information, during the Joomla day toulouse, we have worked with Hikashop and Hikamarket to provide a multisites version of these eCommerce application.

The new functionalities present in Hikashop can filter the product categories on the JMS site ID and with the Hikamarket, have vendors that have their own website and filtered on the side ID.

So, now, it is possible to have a super store that see all the products and information form all the vendor and in the same time have "mini sites" that are specialized on a specific vendor or some specific product categories.