Car rental in Portugal for exploring off the beaten path

[Staind]

I'm planning a trip to Portugal next month and want to rent a car that can handle more than just city streets. My goal is to skip the typical tourist spots in Lisbon or Porto and actually explore the real Portugal. I want to visit those small authentic villages where locals still live the traditional way, see the countryside, maybe hit some coastal towns that don't show up in guidebooks. Problem is, a lot of these places are connected by rough roads or no proper roads at all. Which rental companies in Portugal won't freak out if I take their car on unpaved terrain? I've got two weeks and want to cover as much ground as possible.