You can also use relative snap by the way.
And it seems like the requested feature changed topics like 3 times.
In the ME … You can use ctrl to lock horizontal position as you move note events up. You can also use the arrow key with relative mode on without having to worry about snapping to the grid.
Drums are an entire different issue, but have similar combinations that will work just this way.
The MIDI events in the project window is an entire different issue, but have similar combinations that will work just this way.