No, but you don’t need to.
Your account only works on one server, because all the servers are independent. The server you joined is your gateway into the wider network, because all the different servers talk to each other despite being separately owned.
To use an analogy: you can’t sign in on Yahoo Mail with a Gmail account, but you can still send emails between Yahoo Mail and Gmail because all the different email servers talk to each other despite being separately owned.
You can of course have multiple accounts if you want to, but there’s no technical need to do this as you can follow people on other servers from a single account. People with multiple accounts on the Fediverse typically only do this for non-technical reasons, for example separate work and personal accounts.