You don't need a re-entry permit. Your visa is already multiple entry. If you'd get a re-entry permit, you would keep your current stamp active. That is not what you want, you want to activate a new entry, as it'll be much longer.
You can do that without a visa, but then you need a border run each year to reactivate your exemption.
You might go abroad and back right at 60 days, giving you no flexibility to plan. Or you could use one extension, then you can time your exit more the way you like. And you could combine it with a short trip in the region.