On a cold February morning at the Brooklyn Navy Yard, the skeleton of a modern 15-story building was rising from a muddy construction site along the East River. As long and as tall as a cruise ship, the sleek glass structure loomed above rusty, century-old dry docks, serving notice to the industrial neighborhood that the new economy was coming.

The project, known as Dock 72, is the brainchild of WeWork, the fast-growing New York start-up valued at a whopping $20 billion. In just eight years, WeWork has built a network of 212 shared working spaces around the globe. But WeWork’s chief executive and co-founder, Adam Neumann, isn’t content to just lease out communal offices. Mr. Neumann — a lanky, longhaired 38-year-old Israeli — wants nothing less than to radically transform the way we work, live and play.

When Dock 72 is completed this year, if the aggressive timeline holds, it will represent the fullest expression of Mr. Neumann’s expansive vision to date. There will be an enormous co-working space, a luxury spa and large offices, for other companies like IBM and Verizon, that are designed and run by WeWork. There will be a juice bar, a real bar, a gym with a boxing studio, an outdoor basketball court and panoramic vistas of Manhattan. There will be restaurants and maybe even dry cleaning services and a barbershop.

It will be the kind of place you never have to leave until you need to go to sleep — and if Mr. Neumann has his way, you’ll sleep at one of the apartments he is renting nearby.