I wear thin shirts all the time, but when I do... I usually double bind... even though I only have a B chest to begin with- just makes me feel better and less dysphoric.
I use an old 997 that is stretched out, and a new one over top of it. It's hot as balls, but it works well. I don't wear deep v-necks with the 997.. if you are going to, then you definitely need to get a v-neck binder as nygeel said.