Rafael (and Ronny),
I believe what you're looking for is as simple as adding another server to your environment. You can check how this is done in the platform instalation checklist (according to your platform version); add the new server as a new front-end and, afterwards, change roles with the old server.
Ronny, your task adds another level of complexity, as you also want to upgrade the platform from v10 to v11. Check this document; please consider that the upgrade must be executed in all your environments and it should start with the development environment (where all the breaking changes must be tackled).
Best regards,
Henrique