If you just tack on another full stringer onto the side of your open-cut stringer, realize the balusters would still be inside of that on top of the treads. So keeping a carpeted stair would still require the trouble of cutting the carpet around the balusters, look really crappy, be hard to vacuum, etc.

Otherwise, for a carpeted stair, you would want to move the balusters to on top of the stringer, which would require a wider one equivalent to a wall, but your stair appears open underneath.

The Craftsman aesthetic of your baluster profile were not originally associated with carpet in that era.

How about doing a runner this time around? Your stairs don't look terrible or even dated if they fit the overall style of the house. The style now is simple, which this is. They're square instead of round - they're not builder standard colonial. What do you want to change them to? Do you have an inspiration pic?

The whole place is being completely redone in a ultra modern streamlined style. Don't think the runner would fit with that. Although we are still debating if we want carpeted treads or hardwood. The risers will most likely be painted though.

I guess we are told that without adding a second stringer and more bulk to the outside the only thing that is possible is this:

Remodel by the Beach · More Info

But we don't like the zig zags, and would like to have this look instead:

Cambridge Modern Townhouse · More Info

Ignore the glass baluster part.

And yes, we would put the spindles and the railing on top of the stringer.

The question is: can we build it only up the stringer by adding the missing "triangles" and making it a straight line. Or do we actually need to tack on a whole new stringer on the outside?

Whichever way you do it (on the stair or beside the stair), you are going to be removing the balusters completely and removing and cutting the treads. If putting in "triangles" (which would need to be a cut stringer, not individual triangles) still meets clear stair width, and works with how the stair dies into the floor above (not shown in pic), then by all means go that route if you determine that is the best way. But you will still need an outside cover stringer (a skirt board) over all the "triangle" pieces.

First who is telling what can and can't be done. You need a stair pro to give you the right solution not your contractor .I assume you are replacing the treads so IMO redo the whole thing to your style since replacing the treads is a big job you might as well do it right .

OK thanks. this is super helpful. We are getting advice from a stairs pro, but there's an interior designer in between, and i think things are getting lost in translation. Maybe they meant that the cover stringer needs to get added regardless, and not a whole new stringer. I'm guessing the bulk that will be added is significantly less, if it's just a cover.

Ballusters definitely are going. Not sure if the treads are getting replaced or not.

Here's the end result we ended up with. Old stringer stayed for the structure. New "cosmetic" stringer was built using plywood on the outside of the old stringer. Spindles got installed into the new "cosmetic" stringer, which widened the stairs, except at the top. Railing had to have an S-turn because of that. Kept the old treads since we were going from carpet to carpet, which saved a bunch of money. Painted veneer was added to the risers and also covered the new stringer. Absolutely ecstatic with the end result!

They look nice. Glad you are happy with them.