Your stay in Sagus Cliffs in the early stage of Torment: Tides of Numenera enables us to change our party's composition at will, as we can encounter the individual companions during their mundane activities in different parts of the city. The problem begins with the journey to Valley of Dead Heroes, as the individuals who haven't undergone the airship ride won't be taken to new area automatically, i.e. they won't be found in the areas that are encountered further, making you unable to invite them to the party.
To be able to change your current roster, use the opportunity found in Sagus Cliffs to acquire the Bronze Sphere, an artifact that enables you to "summon" other, inactive party members. Remember that you'll need to find this item before leaving Sagus Cliffs. More details can be found below.
Finding the Bronze Sphere will require visiting Buried Crossroads (a part of Sanctuary of the Changing God - Map 11 (M11), a location that is visited during The Cold, Calculating Jack (visit the adequate section to learn more). Once you've reached the Sanctuary, take a look at the mirrors found in in its central area (M11.8). Interact with it and choose the third action from the menu (Examine the small oval mirror). You should now be able to remove a small object, i.e. the Bronze Sphere itself.
The Bronze Sphere will appear in your story items tab. You can use the artifact at will. To summon a companion, use the Sphere and choose a dialogue option involving the companion that you want to recruit.
Note - If your party is at its full capacity (four people), you'll need to send away one of the available companions before you can summon another person.
Note #2 - Rhin, one of your companions, cannot be summoned once you've managed to help her find her way home (a mission which involves meeting Kwherezimian, found in Small Nihilesh). More details about the event can be found in Rhin's Quest (Companion Quests).