Or double up on stringers?
The only problem with doubled stringers is you're still limited by weight. A mini ridge beam of sorts supported by the concrete posts under the midpoint of the stringers adds more strength at roughly equal cost when you're doing the labor yourself.
Remember basic physics, F = M * A
Mass of wet snow is roughly 20lbs a square ft. Compacted may be more. Also recall that roof is unheated by appearances. We'll ignore any ice load or compacted snow.
Pretend 12 linear ft of the snow off the roof surface fell at once. Now we've got a 240lb load.
Then we can use Mass * Gravitational Acceleration * Distance = Impact force.
9.8 m/s^2 would be gravitational acceleration. To over simplify, let's ignore the sideways acceleration that makes the trajectory an arc and increases movement/flight time. Let's just assume for easy numbers we're looking at, on average, a ft drop from middle of the fall to the ground.
So 240 lb/Sq ft * 9.8 m/s^2 * 3.66m (equivalent of 12 ft) = 8615 N of force at impact per square ft. on the stairs.
6 ft wide that's 51,703 N of force on the 6ft wide stairs at impact for a 1ft deep pile.
One Newton is 0.225 lbs of force. So, that 1ft pile of snow coming off 12 ft of roof surface hits at 11,633 lbs of force in one shot. The lumber isn't rated to take that abuse through the years, which, is how people get into deterioration issues.
(And this post is what happens when someone who apprenticed to an architect a few years before getting into a chemical and oceanographic engineering background reads about stairs and see a sloped roof over them.)
😆
But when you calculate numbers out, they become eye popping.
