Here's what I would do. Cut the support legs where they are the most straight. Use a fine tooth Japanese pull saw or a fine tooth blade in a circular saw. You would need to empty it out and lay it on it's back.
Then make a duplicate of the shape of the supports but 4" longer where it's straight, in a matching wood and attach them on the inside.
You could also use just a straight board without the curved shape since it will be pretty well hidden underneath. Then fill in the missing portion
of the curved section.
As for the back panel, obviously, it will also need to be extended and cut in a location that is easiest to fill, OR just replace the section that is now too short..... my choice.
Four inches will make it difficult, a couple inches could be gained by putting feet under the side supports, you have to be careful to not throw everything out of proportion.
Another option would be to convert top to wall mounted cabinet and just round bottom of existing supports.
This is where you are going to have to be very careful. I would be concerned that 4" would be too much.
I would make the cut/splice at the point where the top meets the bottom. That will only give you one cut that could potentially show. I assume that grain shows, so that will entail making the splice with end grain to end grain. You will need dowels (or some other strengthening method) to make this splice strong.