Proxy backbone/intermediary

I have an account on a proxy service that only allows one IP authentication but i want to be able to have more so i thought about making a server that would play the role of the intermediary and simply handle all the requests i’m sending from multiple machines to transfer it to the proxy service so that i could be able to use the service from multiple machines and with one IP authentication of the intermediary server. I have no idea what are the appropriate Cloudflare product for that or what to do, can you please recommend?