Rerouting All Traffic from One IP to Another?

Hello community!

I have a very weird and specific situation to address. Don't ask why I want to do this, but here it is anyway.

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Let's say I have a server that goes by the public IP: 111.11.111.11, and clients can connect to it.

Now, I just need a different IP address (any other IP address I could find, rent, or use from any source), preferably a server or some sorts. Let's name this IP; 222.22.222.22

I need to route all that's coming from the client (user, for example) to 222.22.222.22, then route it to 111.11.111.11 instead of directly routing all traffic from the client to 111.11.111.11.

Is there any way to do this? Also, I'm looking for something relatively cheap too (if it requires money), because I wouldn't need to do this frequently and I really only need one other IP (besides my server).

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Thanks a lot, please let me know if you have ideas (AWS, or whatever you have in mind!)