Below is a terrible visual sketch of the idea. I had a lot more sketches for that, but I lost the notebook. (Yes, the same lost notebook that is responsible for lost sketches of many other ideas in this database. It was a terrible event :p)

Objective
Cut yourself off from all bad things, attach yourself to all good things.
Input
Tap a character, tap another (adjacent) square to move them. (Or start on them + swipe. Or select + use arrow keys.)
Map & Gameplay
In 3D, with blocky characters, perhaps a slanted (orthogonal?) world view.
General rules:
- When you try to enter a square with another entity, you connect to them instead (but don’t move.)
- Cross lines to cut them.
- Move over something to attach a line to it. Or on top of something.
Different characters have different LINES or ABILITIES. (And there might be different tiles/things in the terrain that change your line when you move over them.)
Is it possible … to include height differences? (Just use the block-by-block movement from Into My Arms, to also make the line a neat and ordered thing.)
Ideas:
- A line that cannot be broken.
- A character that drags other characters with it when moving.
- A line that auto-attaches to anything adjacent to you (at the end of your turn)
- A character that does something automatically (instead of needing your input for it)
Would work wonders as a multiplayer (cooperative 2-player puzzle). You’d just control two characters separately