Yes.
Bluesky limits each user to one active handle at a time but Handles Club has no limit on the amount of handles a Bluesky user can register. Once a handle is registered, it belongs to the registrant forever and the registrant can add it to (and remove it from) their Bluesky profile as often as they like.
Register a handle with Handles Club once then add it to Bluesky as many times as you like.
Interested in the technical details? Learn more in How does Handles Club work?