I’ll start with the obvious. Why does this game need powers? Usually, people do not obtain special abilities when dealing with grief. That is true, but it is also true that this is still a game with a ghost, and I like the characters having special powers.
The real question is how to define those powers in such a way that they help to reinforce the themes of the game while still being fun to use. Why should they be fun to use? Again, because this is a game, and “having fun” is an implicit (well, explicit now) design objective.
First, I set two classes of powers. The first class exist and work only inside the game world, and are called Phantasmagorias. They are more or less “classical” RPG powers, obtained by the PCs and used by them when they want. The second class exist in the game world, but work from the real world, and upon the real world description of the game world, and they are called Death Defiances. They are narrative control capabilities in hands of the players (not the PCs), justified in-game as the ability of the player ghost to defy death and reality.
In Spanish, a ghost is called “fantasma”, and phantasmagoria is “fantasmagoría”. Yes, a phantasmagoria has nothing to do with ghosts, but I liked the word. Of course, having set on the name, I had to justify it: these ghostly powers bestowed upon the PCs work changing reality in a subtle way. Those who see them in use are not sure of what they are seeing, and tend to later think it was just a daydream or a hallucination. And that is the name justified.
Now, I had to decide about the powers themselves. I had the general organisation of the game in the five stages, so I chose to have the powers change based on the current stage of the PC. In each stage, the PC can manifest the nature of the stage of grief spending attribute points.
I also wanted narrative control capabilities, but not unlimited ones, for the players. Following the same basic scheme, depending on the stage of grief of the player ghost, the players can change the narration of the DM (Death Master) spending attribute points of the player ghost. This way, in the Denial phase they can just say “no” to a DM sentence, while in the bargaining phase they have to cut a deal for every change they want to introduce.