Will removing subtreads and risers that are attached with construction adhesive and nails damage the stringer?
I think the least invasive way to handle this is to add two more stingers, one right against the existing stairs(essentially just a nailer) and one out at the ultimate width of the new treads. This way you don't have to remove the old sub-treads/risers or change the height of your treads, which would cause you grief when you get to the top of your staircase. Once you've got your new stringers in just apply sub-treads and riser to match the existing construction and you're good to go. The bigger problem is that no matter how you construct it, the landing or the the lower staircase will have to be modified to make the intersection work properly.  This illustration shows how the problem could be fixed by lengthening the landing and pushing the lower stairs out (assuming you can do this). You could accomplish the same effect by pushing the landing to the right but it looks like your landing is captured on that side in the pictures. Although this fixes the stairs the railing system will still have an unusual transition but it's not too bad depending on how far you need to extend your treads.