@amoroso do you use Firefox as a browser? Use the containers extension ( https://addons.mozilla.org/en-US/firefox/addon/multi-account-containers/ ) and open each account on its own container, on the same webapp. Might solve your problem.

@amoroso I suspect most will. I assume you concluded they don't because when you try to authenticate the second account and you get redirected to the instance to give oauth access, you're already logged in.
But in fact you can log out mastodon and still have phanpy (or any other web app) still keep a valid token.
Adding a second account after logging out the first should work. I don't have two accounts on any instance to test but I tested as far as the logout step.

@amoroso IceShrimp does.