You can't NG+ it until you've fully completed the quest chain. Have you done all 4 roles so far (it's only possible to do those quests once per role)? If so, that does then open an additional 'meta quest' from a new NPC in the bar area where you'll do a series of quests involving all of them - however it's also subject to you completing an old HW quest chain that unlocks all the Containment Bay Trials in Azys Lla for lore reasons.

In the meantime you can visit them in all the zones back where you left them at the end of their quest chains but only to say Hi and get some flavour text.