Hi all, really enjoyed the feed back on my first post, so here I am again with another issue.

The stair well in my home is pretty narrow (less than 3') and has a spot of very low clearance where the second story hall floor cuts across. There have been multiple patch jobs in this area, poorly done... which seems to be a trend within this house

.... Anyways, when I tore out the patch job I found that the 2"X6" joist underneath had been notched to ****. So, now I'm thinking the right thing to do would be to sister another joist to it. Here's my issue: Immediately to the right there is another joist running perpendicular to this one, so the new board would not really extend far (like 6") beyond the notch. Will this be an issue? I suppose that couldn't really make it any worse! The area to the left is open, so I would be able to get the new board to extend fairly far that way...
Also... I would LOVE to get more clearance in the stairwell, but realize it may not be possible... just thought I'd mention it if anyone had any clever ideas that don't involve changing the foot print of the second story. I'm 5'4" on a good day and still have to duck when going up the stairs....
And because pictures are worth a thousand words:
Before:
Half way through, you can see the original lath/plaster on the top half, and dry wall tacked on below...
Notched Joist exposed; the deepest notch reduces the board to 2 1/2". I'm not sure why this was done. Maybe to fit something upstairs?