Is there a way to put together 4 x 4 in the hoop cases together to make larger cases? I realize I would need to sew these on a regular sewing machine and that is fine. Any suggestions?

Yes there is! Look at moosebstitchin.net and go to ITH Eyecases. Sorry I don't have the exact link, but you should be able to google it. You can make any length cases this way.

I am sorry but this makes no sense? Cases? If your machine sews 4x4 that is the largest design it will sew, there is no way to make it do something it was not made to do.
If your question is taking 2 embroidered designs and sewing them together to attach them, yes you can do that on a regular sewing machine. But the above question does not make any sense.