Only place I see that you can add one is the bottom of that stair. Top is impossible die to the partial angled wall and the landing in the middle would extremely dangerous.

Thank you! Do you think it would be best to just add a door to the base and then "bring the ceiling down" above the door to cover the gap since it's quite tall?

A door at the bottom of the stair would require a min 36" landing depth, so you would have to "box out" a little vestibule-like space.

@3onthetree I'm not sure I understand, can you link to a photo example?

Do you think it would be best to just add a door to the base and then "bring the ceiling down" above the door to cover the gap since it's quite tall?

You can add a transom window above the door.

@3onthetree is right - a door right at the bottom of the steps is likely a code violation unless you add a landing area.

You could add the door at the top of the stairs, but you will need to extend the side angled wall on the right and frame up for a doorway on the living room side for an entrance. The extended wall to upstairs will create more of a tunnel felling and darken the stairs going up. Lighting can improve that.

You could try a heavy, lined velvet curtain at the bottom of the stairs. That may be enough to deaden the sound.

That will just look tacky. I agree the only place to add a door is the bottom and yes it will need to be done to code. Maybe it would be better to have the space that creates the noise closed off. Like if a games room for instance could it be framed and closed.

Would it be a code violation to add a doorway in the middle of the middle landing? You would have a 3' landing at the top and the bottom of each set of stairs. Would it need to swing both directions or would it matter?

If building codes don't allow a door to swing over either of the landings could an accordion door work between the two portions of the landing?

If you add a door to the bottom with a bump out to get it to code, consider where the door will be when open. Are there times you will want to keep door open, if so, then you won’t like the door at the end of that opening unless you make the bump out wider than the current staircase. Looks like you could go wider on the right side. Moving the door to a side wall makes moving large furniture problematic. Also, make sure you install a door large enough to get big furniture through. Preferably the door will be as wide as the stairway.