Is possible connect/inject a server in my localhost?

Is possible to ''connect'' a server in my localhost? example: Let's say there is a website, www.xyz123.com, and on this website we have the home page, the numeric ip is 123.1.2.3, would it be possible for me to "connect" and run this website on my localhost? just connect it to my localhost, so let's say I would go to www.xyz123.com, I go to localhost:80 and I would be on the same site, but it wouldn't be mine, it wouldn't be on my computer, it would be the website itself, just being 123.1.2.3 and at the same time 127.0.0.1, would it be possible to do that? in a simpler way to understand, turn my ip into the same ip as the site, or vice versa, to connect to the website through my localhost. * this is just a question I have while thinking about this theory. *