A program which integrates into the browser or standalone icon is Video Downloader Ultimate. Download zip file here. It also offers to convert the downloaded videos into MP4 and apparently supports up to 4K (Ultra HD). Windows only (not Mac).
Unfortunately there is no trial version and the site offers three versions, each with more functionality ranging from 9.99 to 29.99.
Downloaded and installed it. It identified a live stream from Chaturbate but required a code to download.
Verdict: Still under investigation.