(Mostly) natural fiber bra but with cups?

Hi!

I’m looking for a bra made out of natural fibers (silk, cotton, etc) but I don’t love how the shape of these look under clothes when they don’t have cups. Does anyone have any suggestions for bras with cups where the fabric touching the skin is all natural fiber??

I’m okay with the cup itself being polyester as long as it’s lined with cotton or another material!

I’d appreciate any suggestions! I tried ThirdLove but unfortunately their cup is unlined and the foam it’s made of is actually polyester despite that this isn’t disclosed on their website or tags.