Can an appellate lawyer work with my existing trial lawyer instead of replacing them?

Yes. Appellate counsel can function as specialized outside counsel for another lawyer or law firm rather than replacing them. The trial lawyer typically keeps the client relationship and continues running the case while appellate counsel takes on the specialized appellate work: evaluating whether an appeal should be pursued, analyzing the record, researching standards of review, and preparing the appellate brief. The Florida Bar's own Attorneys' Exchange includes appellate practitioners advertising exactly this kind of co-counsel and second-chair availability.