I think most chucks are fitted to backplates so that the mating faces are the ones with the through bolt holes. On 3 jaw chucks, because of the scroll mechanism, the bolts pass through the periphery but on 4 jaw independent chucks the bolt holes are generally nearer the centre so the backplate can be smaller – as on the 4" 4 jaw in the pictures below.
![lrbp1.jpg lrbp1.jpg](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
![lrbp2.jpg lrbp2.jpg](data:image/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==)
So I guess there is a chance that you can fit a 6" on a 4" backplate. However, there is still the issue mentioned above by OMG. The Myford 6" 4 jaw is especially thin with the screw and register machined into the chuck body – there is no backplate so the whole thing fits in the gap. The 4" will hold a piece of 4" square with the jaws turned round .
HTH
Rod