Three years ago, then-Bugatti CEO Wolfgan Dürheimer said the hyper-indulgent brand was looking at four different bodystyles for a second model line. He wouldn’t identify the styles, but they were thought to be a sedan like the 2009 Galibier concept or 2+2 GT, a less extraterrestrial supercar, an electric car, and an SUV. Some rumors of late suggest plans for a “Royale electric limousine” are in the pipeline. Before that, though, Car magazine says “a crossover-influenced sports car” is only waiting for sign-off from Volkswagen Group execs.

As far as we can tell, the phrase “crossover-influenced sports car” is a way to escape calling this reported product an SUV. Remember, brand CEO Stephan Winkelmann said in January that “There will be no SUV from Bugatti” because it didn’t fit the Molsheim automaker’s heritage and disposition.

There could be shades of Italianate wrangling between a boutique brand and a parent company going on here. When ex-Ferrari CEO Luca de Montezemolo said the brand would never build an SUV, he was soon overruled by parent-company CEO Sergio Marchionne. That’s how we’ll get the Purosangue next year, which the Modena sports car maker calls an FAV, for Ferrari Activity Vehicle. So Luca, with help from the marketing team, was technically correct.

Point being that when discussing the shape of the next model, Winkelmann explained needing to balance investment with return, and said, “it’s not me to decide.”

If said proposal gets the green light, it “won’t be a traditional SUV.” The picture painted is of something like a two-door Lamborghini Urus with a higher seating position, much faster bodywork, and much less weight. Underneath would be a Bugatti platform not shared with the rest of the group. Instead of the 641 horsepower kicked out by the 4.0-liter twin-turbo V8 in the Urus, the report says Bugatti would inject some sort of electrical assistance to achieve 1,000 hp.

Winkelmann is known to be against a hybrid powertrain for the eventual Chiron successor because of the weight and space penalties, but a crossover-like sports car would alleviate those concerns. The form factor would also achieve the more livable brief Bugatti’s been talking about for ages, and address global emissions issues such as EV-only zones being proposed in cities around the world.

The model would sit “below the Chiron but on top of every other model,” and cost less than the $3 million Chiron. Production is said to be capped at 800 units per year. The CEO said he would insist on building it in Molsheim, but to do so means expanding production capacity there, and that means more investment, which makes the hottest bodystyle in the world an even more logical choice. Whatever it is, we’re promised “a real Bugatti” and “a reference for other manufacturers.” Even if given the green light today, we’re looking at 2022 or 2023 arrival at the earliest, so you have that long to get used to the phrase “Bugatti crossover.”