Fujifilm's FinePix S3 Pro UVIR does this switcheroo. Both IR and ultraviolet (UV) cutoff filters have been removed from the sensor, so you can use a black, IR passing filter over the lens to block almost all visible wavelengths, and shoot by IR alone.
Unfortunately, you can't autofocus or see the image in the viewfinder with the IR passing filter in place. You can view the image and focus manually with the LCD, but live preview is limited to 30 seconds. And $1,750 (street, body only) is expensive, even if you already have lenses. (It accepts Nikon optics.)