Beastmen of Ator II: Alien Touch

Reverse harem/multiple hero/shifter triad

Major Amber Trujillo is commander of moon base mission III to complete work on the Moon Base. She has dropped the crew and is preparing to return to Earth when she has a nasty encounter with the Basinini—who have a moon base of their own on the dark side of the moon. She has just passed into radio blackout when they pull her out of orbit or send something up to ‘swallow’ her craft and take it down.

The Phoenix Clan have tracked a Basinini craft to the base. They rescue Amber in the course of wiping out their enemies.
They're instantly smitten with the Human woman and decide to take her as their mate.

The problem is the language barrier prevents intelligible communications and they're having trouble getting their message across to Amber--who just wants to go home.