Cable channel AMC last week premiered a new series, “McMafia,” about the global underworld. In the past, cord-cutters who can’t watch AMC could have waited to catch the show on Hulu, where most AMC shows end up. But “McMafia” is headed for AMC’s subscription-streaming service, Sundance Now, a previously unreported sign of how AMC is trying to build its service into a destination.

Tentative steps by a handful of TV networks such as HBO and CBS to build their own subscription-streaming services in the past three years has lately turned into a rush by many. Just in the past few weeks, Viacom and Fox News have announced plans for new streaming services, while Disney is getting close to launching two. The services give media companies a way to reach the growing number of people who aren’t subscribing to cable. And they give the networks more leverage in negotiating program licensing with Netflix and Amazon.