They could go on a journey through space. The male adult could use some advanced alien technology provided by the pet to build a spaceship. Then they could explore different planets, meet other alien species and have all sorts of exciting encounters. For example, on one planet, they might discover a hidden treasure that is only visible under a special light.
Maybe they go on an adventure in a magical forest. The alien pet could use its special powers to communicate with the forest animals. The male adult and the alien pet could team up with the animals to protect the forest from a dark force. They might face challenges like crossing a wide river filled with dangerous creatures or finding a way through a maze - like part of the forest.