Beastmen of Ator Series by Kaitlyn O'Connor

When Cara is taken by the shape-shifting beast men warriors of Ator, she gets hands on training in triad mating traditions.The Furians-Dagon, Gilen, and Joar had lost all hope of a future with the destruction of their home world until they stumble across an Earth woman they rescue from their enemy. Before she can be claimed by a rival beast clan, they decide to claim her for their own and set about initiating the triad mating ritual.

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.