If you loved The Mosquito Coast, try Master and Commander: The Far Side of the World
A bridge between a film you've already seen and one most people haven't. Here's what they share, and what the second one does that the first one doesn't.
You already loved

The Mosquito Coast
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Master and Commander: The Far Side of the World
What they share
Both films are directed by Peter Weir, and they sit in Adventure / Drama territory. If that's the register that drew you to The Mosquito Coast, the second film will land in a comparable space — through a different lens.
What Master and Commander: The Far Side of the World is
You command a British warship in treacherous waters and then a French vessel attacks. The captain's relentless pursuit is matched by the surgeon's concern for the crew. The film is set during the Napoleonic Wars.