I definitely support the notion of allowing "shipping from foreign ports to multiple American ports in sequence." (Shipping from China to Port A, Port B, and Port C in sequence, while allowing off-boarding only of cargo in ports A and B.)
Allowing foreign-flag carriers to ship general cargo among American ports is not something I have a strong opinion on (but I generally am not inclined to permit it).
That is already how it works. Transpacific eastbound ships typically call at LA/Long Beach, Oakland, and Seattle before returning to Asia. They just can't pick up cargo at any of those stops and then drop it off at another US port (they can and do pick it up and take it to Asia)
Then why is Puerto Rico complaining that the Jones Act is causing high prices in Puerto Rico for foreign-sourced goods? Are those complaints just invalid / based on a completely wrong premise?
I think the generous claim would be that given that Puerto Rico has a manufacturing dominated economy, if foreign flagged vessels could pick up goods there and take them on to the USA, they would be more likely to build routes that included them. Eg you could go through the Panama Canal, stop in PR to drop off goods from Asia and pick up goods from PR, and then continue on to Savannah/Charleston/Newark.
Allowing foreign-flag carriers to ship general cargo among American ports is not something I have a strong opinion on (but I generally am not inclined to permit it).