Clipious allows users to change servers, though I admit the option isn't quickly accessible. However, it does not appear to allow saved profiles on the same server IP.

Please consider adding the ability to change login profiles, even if the profiles are on the same server.

I tried setting this up as a different server, but Clipious recognizes the same IP as an existing server. The only workaround I have been able to adopt myself is to create additional Invidious instances. I could see another potential workaround being something that allows a single instance to be reachable behind multiple, distinct IPs.