Closing off staircase, convert into 2 closets

Hello guys, I don't have a picture of the staircase at the moment, but I will update the thread as soon as I get one. What I'm planning on doing is closing off the staircase from the first floor to the second. The house is being turned into 2 one-bedroom apartments, and this will add privacy and storage to each of their apartments. I couldn't find anything online about any projects relating to this and I wanted to get some advice before jumping right into it. I was planning on screwing 2X4's into the existing studs and framing in the ceiling, and using 3/4" or 1" plywood for flooring for the upstairs. Any comments/suggestions are greatly appreciated. Thanks!

 

Welcome to the forums.

Am I reading correctly you intend to use 2x4s for floor joists or is that just for the walls?

 

Are you going to be removing the staircase, or just using the void under it for closet? As Mitch mentioned, you should be using heftier joisting for above floor, as well as joist hangers if there is no resting place for the closet floor joists.