The band makes it tricky!
I think Kathleen M. has a great suggestion with maybe a tissue weight turtleneck, if you can pull of turtlenecks. I love the look, but my short neck and double chin don't, which makes me sad.
Have you tried it with a cardigan that hits within the band rather than above or below? Or a super long one that is almost as long as the dress?
Do you need a topper for warmth? Or are you just wanting to add one so that you feel more finished? I think the dress looks like it would stand on its own pretty well. So yeah, what Aida said!