There is no stated limit. I see fourth and additional bags quoted $100 each for my upcoming transcons.

Some years back, friends were returning to New York from a sabbatical in Italy, and asked my advice on shipping their accumulated possessions. They were out of ideas; a container was exorbitant. I proposed checking everything as luggage. They found a box maker in the hills outside Lucca, who made them a dozen triple-walled boxes to just under the airline dimensional limits.

This will probably remain the only time I pick up friends at JFK in a U-Haul truck. (We went out for Korean BBQ. Of course.)