I think that you have introduced an important distinction: some games let you manage more than one character but not at the same time.
For example, Gray Matter is divided into chapters and in each chapter the player can play only one of the two protagonists. When you play character A, character B is rarely seen/met and even then it is a NPC. This is an interesting design choice, because in each chapter the player is always focused on the only character that can be played and on the tasks that the playable character has to execute.
Broken Age has two playable characters and the player can switch between them in any moment, but the two characters can’t interact or collaborate because they live in two different places and don’t communicate with each other.
Day of the Tentacle has multiple characters: the player can switch between them at any time and they can cooperate, even if they don’t physically meet.
In Nanobots (funny indy adventure game) the player manages six different small robots, each having its own special abilities. They cooperate in real-time to solve the puzzle together. The kind of interaction between PC is very similar to what the player does in Gobliiins.
Ben There, Dan That! has two protagonists, who always go in tandem everywhere. One of the two characters is also an icon and the player can use it to tell that specific character to do something different from the other one. It’s a limited form of cooperation.
The Book of Unwritten Tales has multiple playable characters who can cooperate in some scenes.
Gemini Rue: in each chapter of the story the player manages one of two characters. In this case the characters never cooperate. It is a special case, though, for reasons that I will not specify.
Secret Files: Tunguska: two playable characters. Sometimes you can play only one of them, other times you can play both, switching between them so that they can cooperate to solve puzzles.
To sum it up, all of them are games in which the player can manage more than one character, but…:
Game | Switch any time? | Real-time coop?
Gray Matter | No | No
Broken Age | Yes | No
Day of the Tentacle | Yes | Yes
Nanobots | Yes | Yes
Ben There, Dan That! | No | Sometimes
TBoUT | Sometimes | Sometimes
Gemini Rue | No | No
Secret Files: Tunguska| No | Sometimes
Gobliiins | Yes | Yes
I prefer those cases in which the characters don’t interact between them nor cooperate, but I understand that real-time cooperation can provide a richer experience and nice puzzles.