We get ruffled when the anti-Tesla crowd makes baseless doom and gloom statements against Tesla. No need to reciprocate.
The Model 3P is going to be an amazing car and I'm going to buy one, but nobody in their right mind would suggest its going to out-handle a BMW M3. Nobody who's done an honest price analysis is planning to save a ton of money on a P vs the BMW either.
It can be done, but it will be a surprise if they do. The BMW M3 is not in hardcore track trim, there's meat left on the bones deliberately. It's not like what we have seen Porsche, Ford, and GM do, which is pull out the stops and make a car people won't want to drive on the street. These are made in limited numbers normally. A great example would be the 2014 Z/28 when compared to it's competition of the time. It's 3800lb without driver. It had no AC, single speaker AM/FM radio, fake back seats. If you go up a driveway at an angle, it is so stiff it will lift 1 or 2 tires off the ground. The tires are dangerous in the rain, last 2000 miles, and the
fronts are 305's. These are not intended primarily for street use. 1.08g on a skidpan, and 1.5g braking at low speeds, more at high speeds due to downforce aero pieces.
So you can take a 3800lb car and make it a track weapon. It doesn't even need AWD. But ... it probably would need an expensive change to the rear axle. Either 2 motors, one per axle, or an LSD.
Tesla is not likely to do such a treatment to any of their cars. MFRs build cars like that to prove a point for a couple years, until somebody gets more hardcore. It's more marketing than an intention to sell track cars.
Track-pack price bump depends how bad the MFR wants to 'win'. The Z/28 was 3 times the base cost. So think $110k for a Model S Track Attack variant. This would do it. Carbon ceramic brakes, carbon fiber aero kit for downforce, dual rear motors, spool-valve shocks, weight reduction, lighter wheels, and expensive summer only tires. And a lot of tuning.