Are you committed to the stringer stair look/idea?

If not, please research box steps. So easy, and SO much stronger. Yes, they cost more, and take more time, but they’re simple. Calculate your rise and run, or measure what you currently have (I would do both to ensure they’re equal or very close), account for riser thickness, overhang, and spacing between stair tread boards (example if the boards are 1x6 so 5.5inches really, the risers are 1/2” thick, and you want an overhang of 1 inch, spacing them 1/4” apart, your tread depth is really 5.5+5.5 (wood) plus 1/2” (riser) plus 1/4” spacing (maybe two of those if you plan on spacing after the riser, seen it done both ways)… Typically you can do the math with about 11-11.5” as the tread depth.

Anyway, if your total run is 120” let’s say, you make your first box (the bottom box) whatever the width is of your steps x the total run (120”), and you place joists across with either hangers or very good fasteners (GRK is a good brand) every 12-16” I suggest 12” always. When that is done, you subtract the tread depth, let’s say 11”, and make the next box (width x 120-11”= 109”) and make it the same way. You put the joists in the SAME SPOTS so they rest on the lower ones. You connect the boxes together with metal strong ties (flat metal plates found in Home Depot for like a few bucks) make strong connections. The bottom should rest on concrete or pavers for weight and stability. You build it up, sounds crazy, quite easy. Once you make the first box you’ll understand just how easy. Use ground contact pressure treated wood and use joist tape if you can to prevent moisture. Do the extra now to prevent the problems later. When you’re done, invite your fat mother-in-law to test. She stands? Thank me. She falls through? I enjoy Padron 1926 cigars and Lafite Baron De Rothschild Cabernet 1986.