Sea Robber has Hector in a Danish slaver off the west African coast when his ship is captured by a bunch of buccaneers en route to the South Seas and young Mr Lynch is enlisted to navigate the vessel around Cape Horn, something that will hopefully give him an avenue to be reunited with Maria, whose testimony and the subsequent disgrace of her mistress' husband has seen them relocated to the Thief Islands (Magellan's Ladrones, the modern day Marianas), on the other side of the Pacific.
Having found that out, that's, predictably, where Hector, Dan, Jacques and ex-prizefighter and timbergetter from the Campeachey coast Jezreel are headed. Along the way, finding an emaciated islander adrift on a sinking fishing boat boat. brings them to a poverty-stricken island jealousy guarded by a Japanese warlord.
When they've extricated themselves from that little difficulty, an alliance with the Chamorro, the indigenous people of the Ladrones, and a night raid to release hostages from a Spanish fort reunites Hector and Maria and from there they're off around the edges of the Spice Islands in search of somewhere safe where the young couple can settle down, though safety will necessarily equate to somewhere safely away from Spanish influence.
The quest for a sanctuary will presumably give Severin the subject matter for a fourth Hector Lynch volume, which will presumably get them into the Indian Ocean.
There's no indication that I can see at the time of writing of a fourth volume in the series, but if I had to speculate I'd guess that Hector and Maria will find themselves in some quiet backwater in the Seychelles or the Comoros where Mr Lynch's long lost sister Elizabeth will turn out to be a person of some influence.
Given the fact that I wasn't over-impressed by Corsair, and only grabbed Buccaneer and Sea Robber when I sighted them heavily discounted in one of those el cheapo outlets I don't think I'll be in a hurry to track down the fourth volume if and when it appears.