I once read a book about a spaceship captain that transported multi armed (I think six) humanoids. Thought it was a Daniel Leary book, just read the series and didn't find it. I read this about 10 years ago.
The head of the family had an affair with the captain. He was attacked after they got to her home by her attendants.
Sounds like Starliner from David Drake.
The four armed (but six dugged) aliens are just a side story. The main story is about a star voyage just as war is breaking out between two of the planets it will land on during the trip.
The ship is on a circular route between Earth and several of the larger colonies and independent worlds. Its sister ship/competitor disappears, and turns out to have been taken by one of the warring parties to use as a troop transport - the plan fails, though, when the captured ship crashes into the capitol city of the planet that captured it.
Another group attempts to capture the titular starliner. That attempt fails as well, thanks to the efforts of the first and second officer, the "cold crew" (who work outside on the ship while it in whatever alternate space is used to make interstellar travel possible,) and two old men who turn out to be the most bad ass secret agents you've ever seen (presumably sent by the government of the Earth.)
The aliens book passage on the trip, and the second officer accidentally carries out a mating dance with the matriarch of the clan of aliens. He had learned some of the dances, but the information he had didn't mention that the motions of certain arm pairs changes the meaning of things. Lacking the multiple arm pairs, he uses only the motions for the upper arm pair - which makes a mating dance of what is supposedly just a celebration of the fall season.
This turns into a problem when the ship has to divert and actually land on the alien planet.
The captain actually had little to do with the story. The officers are split into "staff side" and "ship side." The story is mostly told from the point of view of the staff side first and second officers. The captain is, of course, ship side rather than staff.
