"The vast majority of our target consumers have leased a car rather than buying it, rented a vacation home or enjoyed other prized possessions without purchasing them," he said. Watches, Brandoff said "are the next vanguard" in the luxury rental/timeshare world.
Read MoreWill there be a trillionaire in the 21st century?
Eleven James has several different customer plans, depending on the value and number of watches a customer wants every year.
Its "Aficionado" plan offers watches valued at between $7,000 and $15,000, and clients pay $2,700 for three two-month long watch rotations per year, or $4,850 for six two-month long rotations per year. In other words, customers can either choose to have a different watch all of the time or some of the time.
The other plans work in similar fashion, but offer members the chance to have access to more valuable timepieces. The "Connoisseur" plan includes watches priced between $15,000 and $30,000, and costs $4,950 for three watch rotations a year or $8,950 for six watch rotations a year. The "Virtuoso" plan includes watches in the $30,000 to $50,000 range, and costs $9,700 for three watch rotations or $17,250 for six rotations per year.
Paying $9,700 to wear watches you have to give back sounds insane, of course. But Brandoff said that many of his customers want to try out different watches before they sink even more money into a purchase. Other customers, he said, have already spent fortunes on their watch collections and don't want to buy more—but they like the variety of wearing other watches.
Read MoreMeet the 'hand-to-mouth' wealthy
"Most watch lovers follow the same pattern," he said. "The first six months after they buy a watch, they love it. The second six months, they don't love it as much. And by the third six months, it gets put on the pile and replaced by one or numerous others."