So I know that you aren't able to make a close combat attack from a higher elevation to a lower elevation (and vice versa) even if both figures are adjacent to the border, but is it possible to do so if both characters are on the border of the stairs?

I've heard mixed responses from my venue and this question has probably been asked before, but I just need it clarified. Thanks!

My understanding is yes you can. I don't believe you can poison or have to breakaway but I believe close combat actions are fine.

Page 14 of the 2014 Rulebook:
And FatTony is correct. Since they are NOT adjacent (i.e. they only may close combat like that are adjacent), no breakway is required and adjacent-related game effects like Poison cannot be used.

This only works in 1 situation:

2 2 S 2 2
1 1 S 1 1

If the figures are on those 2 squares that are "S" stairs, they can punch each other. However, if the following happens:

2 2 S S 2 2
1 1 S S 1 1

The figures can ONLY punch each other if they are on 2 squares that are vertical from each other on the stairs (meaning no punching across the diagonal).

MikeTheRed beat me to it, but here's the whole excerpt from the rulebook:

Thanks guys, I searched the rulebook, but not well enough. This helps a lot, thank you again.

It's also cool to remember that Leap/Climb allows a figure to attack an opposing character on different elevations! Fun stuff!

Punching across the diagonal on larger stairs is perfectly legal.