This isn't currently possible. You would need to render two images and composite them together. Perhaps the second image could just be this one object that's different. If other objects partially block the object of interest then it becomes slightly more complex. You can render the object with the overlapping objects if you give them a Constant Shader with its colour set to 0 and its alpha set to 0. This will cause the overlapping objects to appear black in both the RGB image and in the Alpha image, allowing you to composite the object over the first image.
To save an alpha, press the 'A' key in the Render View to view the alpha image, then click on the Save button. Alphas can also be saved when you render an image sequence, using "Extra output images".
Matt