CBS Corp. Chief Executive Leslie Moonves, who last week also became executive chairman, is using his expanded influence at the network to build a greater presence in the digital television realm, Reuters reported Monday.

Moonves is looking at planning more original content for its subscription-based CBS All Access service as well as taking some of his network’s shows off the air and putting them exclusively on the service. This would potentially make CBS more competitive with Netflix Inc. and Hulu.

The network’s push to ramp up its online CBS All Access service, which offers its shows on PCs, tablets and smartphones for $5.99 a month, comes as media companies are rethinking their business models and their relationships with streaming video providers, treating them more like competitors than allies.