Centering Camera Viewport Rect?

I have a Camera and I would like to render a portion of its view whilst maintaining the objects current position on screen. So - for example:

I have a view with a couple of objects in it like the below image: http://s4.postimg.org/rzaqyr3ot/Image1.png

I would like to render a portion of the view whilst maintaining the objects onscreen positions - like this image: http://s2.postimg.org/l4z6x5lbt/Image2.png

The problem is that modifying the viewport rect centers on the object (for obvious reasons) thus adjusting their onscreen position like this: http://s2.postimg.org/xyx8qhyrd/Image3.png

Does anyone have any tips for how I might go about solving this?

Thanks in advance!

George