You can get whatever exposure you want. Put the camera in manual exposure mode and select the ISO, aperture, and shutter time you need to get the result you are after.

To alter the relationship between the brightest and darkest elements of the scene you should adjust the camera's contrast control(s) if you are saving your images as jpeg files.

If you are saving the raw data you will have much more control over the brightness response curve in a post production raw conversion application such as Lightroom. You can boost the shadows and reduce the highlights in addition to adjusting overall contrast. Or you can adjust the light curves themselves (this has a steeper learning curve, however).