This page discusses what hosting companies support domain mapping.
We know of the following hosting companies that are compatible with Domain Mapping System.
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.
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
VULTR (w/ CloudPanel).
Any hosting company providing cPanel access with an Aliases option.
Any VPS or Dedicated Server with root access.
WP Engine (confirmed by customer).
Unsupported Hosting Platforms
Any managed host that does not allow mapping of multiple domains to a single WordPress installation.