Sure, it can be done, but you're not going to like the number, I promise,

thanks! Approx?

X2 what Joe said, it can be done and It will be expensive... by saying expensive what is expensive in your eyes...just the railing (if it's oak) material cost is costly, now you have to cut/remove the wall, prep for railing, install the railing, most likely you will have to replace carpeting on the stairs,etc.

As the cost goes depending who does the work and the railing style you choose. Out of the sky number set your budget around 6-8k...

Your best bet is to get a few stair guys in there and get a few estimates and compare apples to apples.

Probably less than 10K.

Good luck getting any stair guys in there. I quit bidding stair jobs; couldn't get the money. Take them a picture and a drawing with dimensions. And beg.