When I made my ruffled chemisette last year, I set aside a long strip to use later for a removable double ruffle, which I have now completed:
It was very simple to make. I rounded the corners and hemmed the edges with a hand-rolled hem. Then I pleated it to match the circumference of my neck and stitched it by hand to the center of a length of 1/2" wide twill tape, leaving long enough ends to tie in a bow.
I simply tie it on around my neck above the chemisette, and because it's the same fabric it blends in and looks like it's part of the overall garment. Here's how it looks in action:
It makes such a lovely frame for brooches, like this gorgeous hand-carved cameo that Brian the Engineer bought for me in Italy:
I love it because it adds just a bit of extra depth to the chemisette, so it's like a whole new piece without making a second one. Also, I can easily remove it if it becomes uncomfortable (I tend to have an aversion to wearing anything tight around my neck) without removing my dress.