Girls in the midwest have been doing this for ages! Ever since the spaghetti-strap tank tops came into fashion (and the slip dresses) I have seen girls wearing a skinny tee or a sleeveless top under a strappy, skimpy tank-top. That way you can still wear your bra, and if you have back-acne (like I do) you don't have to expose it to the world.
I am quite fond of this look myself, because I have some excellent tops that are too skimpy for work, but can be paired up with other stuff to be more modest and more funky at the same time. I can wear a long, but strappy tank top under a cropped, long-sleeved top, thereby covering my stomach and chest, yet showing layers of interesting fabric. Or I can wear a short-sleeved, skinny tee under a sundress that would otherwise be too revealing for work. Then it is more like a pinafore dress and rather Loli-Chan, especially with my big, black boots and my hair in french-braided pig-tails.
It is fun, too, to combine colors you wouldn't otherwise think of, like orange and electric blue, or yellow and purple. Plain color, bright tanks and tees can be a good and cheap way to express your love of color and you can pull it together with outlandish accessories. I have this great rainbow-striped belt that had been my mom's in the 1980s that I use this way, and lots of wild earrings from my junior-high years.
Layering is definitely a great wardrobe extender and is incomparable for versatility.