This page discusses what hosting companies support domain mapping and alias domains.
If your hosting platform offers support for Domain Aliases or to control the Domain Root for each domain handled by your server, then you should be able to setup Domain Mapping System properly. That basically includes:
Any hosting company providing cPanel access with an Aliases option.
Any hosting company providing a custom platform that allows Alias Domains, Addon Domains, or Additional Domains to be served for your WordPress site.
Any VPS or Dedicated Server with root access.
Anybody can setup Domain Mapping System with the right server access, whether you're using basic shared hosting, VPS, Dedicated Server, etc.
Managed WordPress hosting companies generally will not support multiple domains mapped to a single WordPress installation, but there are exceptions.
We have no affiliation with any of the companies listed. We have received requests from many users of Domain Mapping System over the years, and these are the companies we've verified are either fully supported or not.
Supported Hosting Platforms
We've confirmed the following hosting companies are compatible with Domain Mapping System.
InMotionHosting via cPanel (confirmed by developer)
Cloudways w/ Digital Ocean (confirmed by developer)
GoDaddy (confirmed by developer, requires their proprietary cPanel access)