The list of entries I need to grab is available here:
http://arcresources.mediaroom.com/api/newsfeed_releases/list.php?format=json
Each individual entry is available at a unique URL, by adding an ID, like so:
http://arcresources.mediaroom.com/api/newsfeed_releases/get.php?format=json?id=n
Is there some way to get FeedMe to create entries for every ID from the list URL, using the get URL?