Bugatti will auction its one-off Chiron Profilée this week, giving the world’s wealthiest car fans their last ever chance to buy a brand new W16-powered Molsheim missile. The entire Chiron production run is sold out, so lot 177 at RM Sotheby’s Paris sale on February 1 really is a fairly significant sale.

The car itself is also pretty special. Designed in response to customer requests for something more extreme than the Chiron Sport but less track-focused than the Pur Sport, it could have spawned a short production run, but Bugatti had no spare production capacity so it ended up being a one-off.

The Profilée name was borrowed from aero-conscious cars from Bugatti’s back catalog and the modern version also features a similar upswept tail not seen on any other Chiron. It also features a unique design of alloy wheel and a special color scheme that fuses a light Argent Atlanique silver blue with a Blue Royal Carbon tint for the lower sections of exposed composite bodywork.

There’s more blue in the cabin, which gets special woven leather trim on the door trims and center tunnel to deliver a far more luxurious feel than in the Alcantara-covered Pur Sport. But the two hypercars are more alike under the skin thanks to the Profilée’s suspension setup, which features stiffer springs and more negative camber than the Chiron Sport.

Related: Bugatti Chiron Profileé Is A One-Off Pur Sport That Doesn’t Skimp On Luxury

 One-Off Chiron Profilée Is Your Last Chance To Get A W16 Bugatti Before The End

Both the Profilée and Pur Sport use the standard 1,479 hp (1,500 PS) quad-turbo W16 engine fitted to the base Chiron, rather than the 1,578 hp (1,600 PS) version found in the Super Sport, and Centodieci. But they also get a shorter final drive that gives them much snappier acceleration, while the Profilée’s more slippery shape gives it a 236 mph (380 kmh) top speed versus 217 mph (350 kmh) for the Pur Sport.

The 60 examples of the Pur Sport cost $3.6 million, but the Profilée’s one-off status means it’s going to smash past that figure when the hammer falls this Wednesday. What do you think it’s going to sell for?