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You must still have registered (own) all of the domains.

Your host must allow you to have multiple domains associated with your hosting account. This is usually called Add-on Domains. If unsure, ask your host.

Have all of the old domains as this kind of “add-on” domains in your hosting account.

Make sure the DNS nameservers for the old domains point to the nameservers of your site; you may have to ask your registrar and your host to help you with this.

Following the above you have a site which can be accessed from multiple domains. However, you only want your site displayed and listed as a single domain. This part is possible with Admin Tools' .htaccess Maker.

Go to administrator, Components, Admin Tools for Joomla, .htaccess Maker. In the “Redirect this (old) domain name to the new one” setting list all your old domains, separated by commas. For example www.example.net, example.net, www.example.org, example.org . Do NOT include the domain name you want to server your site with.