I have a 2013 Mini Cooper Hardtop S, 6-speed. Should I buy the extended maintenance package?

We need to differentiate between 'maintenance' and 'repair insurance' If you mean a plan the you get oil changes, all the stuff outlined in the scheduled maintenance is one thing, and depends on how much it costs and what is included and what the deductibles are. Most of these plans do not cover hoses, belts, brakes and such. They also have high deductibles, what they do is know the average cost of repairs over that time, and charge double or more, that's how they make money. They are not looking out for you, they are out to make a buck. Usually, if you set aside all the money you would pay for the extended warranty, save it, and use it for problems that arise--you come out ahead.