Greg wrote:
I'm a painter, for the last year or so all the builders here use 2 -
2"x12"s notched, with 2 - 2x12" uncut nailed to the outside of them, so you
are putting up two stringers, double thick, one notched, one not.

That certainly adds sufficient strength and stiffness. What I don't
like much about doing it that way is the ends of the steps are butted
against the outer stringer and thus become a water collection point
plus here where the wind blows, "stuff" tends to collect in those
corners.

For those reasons, I still prefer the third stringer and if use the
double stringer, make it narrower so treads still overlap.

End the end, personal preference rules, but definitely OP needs more
than just two...