Douras
After meeting him at the very beginning of the game, later you will find him in Goliet - the ruins of the hotel. After you are asked to figure out the cause of Ascor's death, you will find out that it is Douras who is the culprit. If you choose to side with him, he will join you forever.
Arx
Unlike Duras, Arks doesn't need to complete a quest or anything like that. You just need to find him near the Dome City and talk to him, after which he will join your party.
Falk
As with Arx, there is no quest for Falk. You just need to find it at the very top of the Transformer in Edana. Talk to him and he will join your ranks.
Beast
In order for the Beast to join your team, you need to find her in the Fort and complete the "Evil Lady" quest. Since the Beast will ask you to defeat the monsters and El Kolosaro, I recommend completing this task with an already pumped character. Once you're done, you need to see the Bestia again and add her to your companions.
Crony U-4
For this companion, you need to complete the "Maintenance Protocol" quest - at the very beginning of the game or after you find this drone in Goliet. Please note that the specified quest is difficult, so prepare well.
Kaya
You will find her in the Dome City. Talk to her to start The Chosen One. After that, you will meet her at the Main Gate. Ask her to join you and she will.
Ray
Ray is in the Sand Pines Motel, and in order to get him into your party, you must complete the quest "For a Handful of Shards" for him.
