I'm challenge by this situation and the only way I have worked out how to do it is to use the mouse to click into another cell.
What happens is, after I have made a selection of one or more options from a drop-down list, the following keyboard commands result in undesirable effects:
Tab or Enter while mouse is hovering over list: selects / deselects list item
Tab or Enter while mouse is hovering over cell: sometimes adds another selection, other times removes all selections
ESC: loses the selection (same as Excel would)
Is there another key that would keep the selected items and move me to the next cell in the row?