It's a possibility, You will be removing the entire side plates first right? Making a full penetration weld the entire length of the plate, about 3" from one edge, not in the center of the entire plate, could be asking for problems with it warping and bending. That said, I expect it can be done with some careful welding and possibly hammer work once done.
If you try to trim the bad part off in place, and weld new on in place that is a lot of work too, and you won't get all the rust out from between the old parts.
I know steel is expensive, but considering the aggravation, welding time, and quality of the final product, I would go with the entirely new side plates.
All depends on what you want?
Grigg