Rear seats and a big trunk aren’t the usual AMG USPs, but then the GT four-door coupe isn’t your usual AMG. Better known for extracting seemingly never-ending amounts of horsepower from their hand-built engines, this new machine owes its existence to the fact that AMG boss Tobias Moers has children to transport from time to time. And you can forget the E-class and CLS, not when another niche has been spied on the far horizon, one that fulfils the brief fumbled slightly by the technically impressive but inelegant Porsche Panamera.

The GT four-door coupe is the third model developed entirely by AMG, following the SLS and GT coupe and convertible. All the things you would expect from these paragons of power are present and correct, principally the 4.0-litre ‘hot inside V’ V8 biturbo, which delivers 630bhp and 627lb ft from 2500 to 4500rpm in the GT 63 S. There are other engines: the same unit in non-S form makes 577bhp, and there are also GT 53 and 43 versions, which use the new 3.0-litre inline six-cylinder in 423 or 357bhp forms. Key to these is an integrated hybrid EQ Boost electric motor that handles starter-alternator duties for improved efficiency and smoothness, and also generates the power for the 48 volt on-board electrical system.

Does anybody rival AMG when it comes to turbo engines that actually make you forget about normally aspirated engines, even for just a moment? Perhaps only Ferrari, whose 3.9-litre twin-turbo V8 gets close to this AMG unit in terms of performance I and I character. This is an insanely clever piece of work, whose technology assiduously helps it avoid the constrained throttle response, noise and lag issues, however slight, that can still blight a turbo. It certainly sounds all kinds of awesome, all the more so with the sports exhaust in full play mode.

Of course, this is also meant to be a daily driver, which is arguably just as big a challenge for a car like this. We tested it in the US, whose freeways can be a seriously mixed bag: the GT 63 S is much more compliant than the GT coupe, smooth riding and quiet, despite its fat rubber (our car rode on 295/35s rubber at the rear, wrapped around 21in wheels). At this point it’s worth noting that the new car is based on Mercedes’ MRA platform (which underpins most of its range), not the GT, and that the badge is a rather disingenuous marketing-led misnomer.

We’ll forgive it this transgression. Besides, AMG was still confident enough to let us try the four-door – all 2045kg of it – on the Circuit of the Americas, the Formula One track near Austin. That’s 20 corners and 3.2 miles, with a serious rep for not suffering fools – whether mechanical or human – gladly. The GT four-door’s technical spec is exhaustive: air suspension, adaptive damping, active rear axle, electronically controlled rear-axle diff lock, with dynamic engine mounts, and fully variable all-wheel drive. The nine-speed dual shift ’box has ultra-fast shift times, while steering, suspension, engine and transmission parameters are all controlled by the Dynamic Select drive system, which spans six set-ups from Slippery through to Race. There’s another programme within even that, the result being an entire phalanx of software and algorithms potentially running rampant.

Potentially. But in reality, the GT four-door has all the bases more than covered. Despite its weight, it changes direction with incredible poise, whatever speed you carry into CoTA’s numerous high-speed corners. Engage Race mode, disable the ESP, and it’ll also go sideways all day long, a process that’s helped by a long wheelbase. The standard brakes use huge 390mm diameter discs, grabbed by six-piston callipers (ceramics are an option). So it stops as convincingly as it goes.

It’s equally persuasive inside. The GT four-door’s cabin is dominated by Mercedes’ widescreen cockpit, which combines two hi-res 12.3in screens whose bonded glass and design are as good as anything made by Apple. Three different instrument configurations are available, Classic, Sport and Supersport, and the main multimedia functionality is displayed in vivid resolution on the central screen. There’s also a new AMG Performance steering wheel, with extra buttons located in the right and left lower spokes controlling the drive mode and sports exhaust. A revised central ‘bridge’, now uses recessed TFT displays rather than actual buttons. There’s no rotary controller, either; instead, there’s a touch-sensitive track pad. Like all this stuff, it’s jarring to begin with, and time and effort eventually make it second nature. Eventually…

The GT four-door can be ordered as a four- or five-seater, and there are multiple USB connections, temperature controlled cup-holders, and if you’ve gone for the two individual rear seats a touchscreen in the middle. Befitting its ‘lifestyle’ aspirations, the GT four-door’s air con, seats, and lighting can all be connected for ‘improved driver fitness’. AMG has even developed its own fragrance, an ‘appealing, sporty scent’. This might be a brand extension too far.

Especially as the core business is in such fine fettle. Of the cars masterminded solely by AMG, this is easily the most rounded and capable. Expensive, of course, but worth it. As is the GT63 S, which gains more power, the electronic diff lock, bigger brakes, the Race mode, dynamic engine mounts, and the astounding 3D Burmester 23-speaker, 1450-watt surround sound system.

If you thought that a five-metre long, four-door body, and hefty kerb weight, would neutralise this car’s performance and handling aspirations, well think again. This is a car of remarkable character and ability.