[john.gersh]

Here's a kludge that seems to work:

Put a magnet in the center of a 2x2 grid unit rectangle; the 1/4 snaps let you do that. Make the rectangle invisible - no fill, no stroke. That gives you, in essence, a portable magnet that snaps to the grid. Place it where you want it in your shape. Duplicate and place until done. Group the invisible rectangles and the shape and make sure "connect to its components" is checked for the group.

The only tricky part is that you can select the invisible rectangles only by dragging across them; there's nothing to click on. If show extras is on, though, you'll see the magnet, so you know where they are. Of course, you could make them invisible only after placing them, but that adds an extra step.

If there's a concern that the magnet carriers might extend the boundary of the group beyond the original shape, you can play around with other shapes as carriers and other places for the magnet on them.