Unfortunately, I don't have concrete data. I should have been more careful to recommend that the author start testing with one post per day, and measure from there.
It does depend upon the page, though. If your posts get high engagement, it will have higher distribution. Of the author's 55k fans, only 14k fans are "talking about" the page, so they'll have less than full distribution. To be frank, their posts are not getting many likes. Thus, my recommendation to just do one great post per day. Also, I would suggest to the author to experiment with photos and not just links with photos. Facebook's push toward bigger photos in the feed is no accident -- they work.
There are definitely brands that have multiple posts per day, and it's largely because of the high engagement their posts drive. Two examples that I follow are "I Fucking Love Science" and "Humans of New York." They both have fewer fans than talking about, and both post multiple times a day. Because their content is highly shared, it gets great distribution. It also depends on your own engagement with the page too, as I understand it.
The best practice I hear about Twitter is to indeed publish multiple times a day. Because it acts more as a true feed and not a digest, repeating the same content at a different hour is considered to be good.