The crossover will become Seat and Cupra's flagship model and is separate to the battery EV model also planned for a 2020 launch.
Based on the next-generation Leon platform, itself a version of the Volkswagen Group's MQB underpinnings, the car has been designed with a low roofline and "exciting styling".
"The crossover was first designed as a Cupra, but we will also sell it as a Seat, because we need the volume to make the project viable," said Seat boss Luca de Meo.
Seat technical chief Matthias Rabe said new plug-in hybrid powertrains – the first of which is due in the new Seat Leon in 2019 – would be configured with several 'system' powers (describing the combined output of the internal combustion engine and electric motor).
Cooking versions of the plug-in hybrid will have total outputs of around 200bhp, but performance versions will be even more potent.
"I don’t want to say exactly, but more than 300bhp maybe,” said R&D boss Matthias Rabe.
Such an output would make the range-topping version of the crossover more potent than the recently revealed Cupra Ateca. That car is powered by a 296bhp version of the VW Group’s EA888 2.0-litre turbocharged engine and can reach 62mph in 5.4sec.
However, de Meo added that, by the time the Cupra crossover is launched, outright horsepower may not be the main marketing and performance benchmark.
"We are looking at badges and names. But you know 0-60mph or acceleration may be a better measure," he pointed out.
The Cupra brand was officially launched at the end of January and it introduced its first model, the Seat Ateca, at the start of this month. The stand-alone performance division has also previewed a hot version of the Seat Ibiza in concept form, as well as a concept all-electric racing model based on the Leon called the e-Racer.