Will three pairs of 12' 2x4 lumber provide a safe work platform for one person?
Long story short: don't do it.

Some of the most dangerous words you'll ever hear:  "Aww, that ain't going nowhere."  Over the years I have seen a lot of mishaps with homebuilt contraptions.  

I am still not super clear even after you added to your description, I get the gist but the details are very important and you're way short on details for my taste.  It sounds like you're building a scaffold or temporary floor over your basement opening to work on the ceiling above.  You're going to build it with doubled 2x4 joists spanning 9'.  Assuming the width of the stairwell is about 3' they'll be about 18" apart.  

In construction you usually use span tables to determine the distance you can span with lumber.  You can do engineering calculations but that's a lot more work, and error prone.  Your scaffold / temporary floor won't be constructed like a real permanent floor so they don't really apply, but they still shed some light.  Here's a link to some span tables, they are not hard to find online:  

https://up.codes/s/allowable-ceiling-joist-spans

Now 2x4's are never used as floor joists any more, so the span tables for floor joists don't help, they start at 2x6's.  However 2x4's are still used for ceiling joists, and ceiling joists support attic floors.  The span tables for an attic with limited storage allow right around 9' of span for 2x4's spaced 16" on center, depending on the grade of wood.  So with doubled 2x4's, I really don't think a 200 pound man on a ladder is going to snap them.  

However I still think it's a bad idea because I don't think snapping the lumber is the main danger here.  I think the most likely trouble is fastening this temporary floor / scaffold to the permanent structure securely and safely.  You haven't discussed this at all.  With the heights involved just about any accident that happens will be a serious accident, so I would not attempt this.  

If you google "stairway ladder" and "stairway scaffold" you'll see that there are lots of options available to do this kind of work without trying to build something yourself.