While the cable industry wonders how many of us will be willing to cut the cord and do without a traditional television package, its online rivals have moved on to a more timely question: How many cords — albeit invisible, cheaper cords — will we be willing to pay for at once?

FilmStruck, an ambitious new movie-streaming site that began on Tuesday after a two-week delay, is betting that you’ll open your wallet for at least two content providers, and possibly three or more. It wants to be your second buy after a larger, general streaming service like Netflix, Amazon Prime or Hulu — or your third, if you’re keeping cable — and it hopes that an increasing number of people will find the money for multiple subscriptions.

Jennifer Dorian, general manager of Turner Classic Movies, which developed the site in partnership with the Criterion Collection, said internal research showed that the people most likely to pay for FilmStruck’s offerings of independent and art-house movies were paying for cable TV and another streaming service. “They’re already very involved in entertainment,” she said. “It’s their hobby, and they don’t mind spending money.”