JMS is able to provide website for different domains.
So have 3 websites with 3 different domains is absolutely possible.
To be able see the same products between the different website, you need to share the products between the websites.
With JMS, you can share some eCommerce extension like VirtueMart and HikaShop.
We recommend using HikaShop because when HikaShop and JMS are present, it is possible that have a partial sharing between the websites.
See the list of extensions defined in the JMS Tools menu and also the one for which a sharing is possible.
www.jms2win.com/en/list-of-extensions?vi...id=269&Itemid=53
Concerning the sharing of the session and remain logged, this require to add the Single-Sign-In for domains.
www.jms2win.com/en/joomla-multisite?page...51&category_id=1
I just see a potential issue with the check-out from any website that would compile the buy from different sites.
Some extensions are using cookies to store the shopping info and in this case, the information will not be shared because in general the cookies are readable for a single domain.
If the shopping info are stored in the session, this could works when the SSI is present as this requires to make the session shared between the domains.
The additional requirement will be to have ALL the product shared between the website and the feature of the "Partial Sharing with HikaShop" should not be used.
So in theory, if you combine JMS and the Single Sign-In with a full sharing of the extension like HikaShop, this should works.