This may be the most useful garment in your closet (there is one in your closet, isn't there?).
The grey cashmere cardigan is great with a white shirt and a black pencil skirt, open or belted; over a strapless dress (any color), or my favorite way, with a white tee shirt and jeans.
You may think "grandpa" at first, but the current styles are more fitted and there is nothing old-fashioned about them. There is even something classic/sexy about wearing one with the sleeves pushed up, the top and bottom two buttons unbuttoned, no shirt underneath, with broken-in jeans.