Bill, the way I would go about this is to, when you go into EDIT mode, convert your multiple point (I'm assuming) graphics that you want to drag at the same time into a single Graphic, using the Multipoint geometry, then enable the Draw toolbar on that single Graphic. When you're done moving (the user indicates they want to leave Edit mode), you can take the geometries in your Multipoint and convert them back out to individual point Graphics.

The way I would go about this is to, when you go into EDIT mode, convert your multiple point (I'm assuming) graphics that you want to drag at the same time into a single Graphic, using the Multipoint geometry, then enable the Draw toolbar on that single Graphic. When you're done moving (the user indicates they want to leave Edit mode), you can take the geometries in your Multipoint and convert them back out to individual point Graphics.