Rain is falling in the Austrian Alps, and for a moment the clouds clear, revealing a panoramic view of Innsbruck to the north and the Tuxer Alpen (or Tux Alps) to the southeast.

Here we climb into the Mercedes-Benz GLS, the new large SUV that replaces the outgoing GL. It doesn’t look drastically different on the outside, but the seven-passenger SUV has been reinvented as the S-Class of SUVs with an updated design, more technology, and a plush cabin.

In the United States, four variants of the GLS will…