Fall Down the Stairs

[Bobbert]

I am pretty sure I have heard Mexicans say:

Me caí de las escaleras

and not

Me caí por las escaleras

I would appreciate someone verifying what is said in Mexico.

Also, which, if any, would a Mexican say:

Me caí de tres tramos de escaleras
Me caí tres tramos de escaleras
Me caí por tres tramos de escaleras

[AngelicaDeAlquezar]

You're right, that's what we say. It's just usage I had never thought about. Maybe we just think about the fact that we roll down while the stairs stay in place.
We also say: "Me caí en la(s) escalera(s)"

I don't know how we would emphasize how long the fall was, but maybe some explanation after saying you fell from the stairs.
For example:
- Me caí de/en/por las escaleras. Me fuí tres tramos para abajo.
- ... Me llevé/resbalé tres tramos.

Your last two proposals aren't wrong, and they would be understood in context.
However, if you say "me caí de tres tramos de escaleras", it could be understood as if you didn't roll down the stairs, but you fell off the stairs from that height.

Now, I hope you didn't fall, but if you did, are you alright?

[Bobbert]

Thanks for the explanations, AngelicadeAlquezar.

Thanks for the concern, but I didn't actually fall down the stairs.

[AngelicaDeAlquezar]

Good to know.