That is a CLASSIC look. I like simplicity. Outside: would be a long coat or trench and scarf. In side maybe a bold necklace OR bracelet. but not both.
Also that clutch is TDF, however I love BIG bags. A statement designer bag (gucci, MJ, LV...)
You can do a lot with a dress such as this. Add a scarf or a belt or a vest over the top. You could even go crazy and add all 3 Bring some color in with your shoes and bag. I tend to stay simple as bags and shoes suggested. Personally, I would add a long strand of pearls, a watch and call it a day.