cname record - How to point multiple top domains to IP of another top domain?

Lets say I have top domain

domain-X.com with DNS A record pointing it to IP 1.2.3.4

then I have domains, which I might not have control over, they belong to customers, which owns them and may have different providers etc.

domain-A.com, domain-B.com, domain-C.com

and I want these three domains to also point to IP 1.2.3.4 but I don't want to set the DNS A-record for each domain to numeric IP, but rather somehow to point them to "the IP of domain-X.com" ... is this possible?

It needs to work so that the application on domain-X.com knows from which URL (domain) the request originated (domain-A.com) and also the user should still see domain-A.com/something NOT domain-X.com/something in the browser.

Is this possible? If not, what other solutions are there? The problem is that there might be more domains then 3 and I want to point them to one IP address where web application serving these domains will be. The application needs to know the origin URL of request. But when the IP changes (because for example I will have to move the app from one VPS of one ISP to another ISP etc), then it could be very problematic to change DNS records in all these domains...

Thanks for any tips and help.

EDIT: Suggested answers to set CNAME domain-A to domain-X are not correct answers, because CNAME record can't be set to top domain (only sub domain) without problems. See CNAME for top of domain?

EDIT2: The links to possible duplicates are also not helpful as they assumes that I am in control of the DNS records of all domain-a/b/c/etc domains. In fact each domain may be owned by different client/customer with different provider. All I want is to make it easy to point to my IP where my webapp is running, and avoid problems in the future when/if I would have to move my webapp to different hosting etc. Then changing all the DNS records could be problematic...

I just discovered that something like "Virtual IP" exists. Could this help?

Another idea coming to my mind is... to solve this from different angle.. what strategies are there to have one IP for very long time?