Overexposing isn't so much changing contrast (although the response in the highlights does start to flatten out due to being on the shoulder of the curve) -- your balance between key to fill is remaining the same. It's just that you don't like the fact that by overexposing the highlights you've also lightened the shadows equally.
So what you're really asking is how you can increase contrast so that the shadow detail stays darker.
You can increase contrast by changing the key to fill level. If the key and fill are natural light, then you'd have to darken the shadows somehow, maybe with negative fill and by shooting darker toned objects, backgrounds. If the key is artificial, then you can increase it relative to the fill, it's just that outdoors, that implies an artificial key that is hotter than the real sun (which is possible, just not very comfortable for the actors.)
Otherwise, you're talking about increasing contrast in post or with the film processing. Push-processing adds a little contrast. A silver retention process to the prints will darken the shadow detail. You can add more contrast in the color correction in digital post.
You could shoot on color reversal stock, which has a limited dynamic range. You won't be able to overexpose as much, but your shadow detail will drop off more rapidly.
If you don't want to go as extreme as reversal stock, you could test Fuji's 160T Vivid stock color negative stock, which is a little contrastier than normal color negative. Their 64D stock is also a bit more contrasty than normal.
