There's no such functionality with the 5D Mark III.

The 7D Mark II and 5D Mark IV (and maybe other newer models) have something almost like what you're asking. If you 1) swap lenses to one with a narrower aperture, 2) add an extender (which raises the maximum f-number), or 3) use a zoom lens at a focal length that has a narrower maximum aperture than what the camera is set to in Manual exposure mode then the camera can alter either the shutter speed or ISO value to compensate. There is a custom function option that allows the user to disable the feature, use ISO to shift, or use Tv to shift.

With the 5D Mark III the closest you'll get is to use Program mode. To alter exposure you can use the Quick Control Dial on the back of the camera to set Exposure Compensation. You can lock in a particular EV by pressing the AE Lock button (the button next to the AF-ON button marked with an "*"). You can then shift Tv and Av in opposite directions by moving the Main Dial just behind the shutter button.

If you press and release the AE Lock button, as long as the viewfinder is active the camera will maintain the same EV as you shift through various combinations of Tv and Av. Once the viewfinder becomes inactive or you press the shutter button all the way down to take a picture the EV is reset the next time you initiate metering or AF to activate the viewfinder. You can also press and hold the AE Lock button to keep metering active and maintain the same EV indefinitely (or at least until the camera's battery is exhausted). The locked EV will be maintained for as many frames as you choose to take while holding the AE Lock button.

You can also choose one of several metering modes that may get the initial Exposure Value selected by the camera closer to what you want. Spot, Partial, and Center weighted average metering modes will move progressively from the smallest spot in the center of the frame to the largest area. Evaluative Metering uses a library of scenarios to determine which area of the frame should be neutrally exposed.