Is $8,000 to rip out and rebuild deck stairs a fair price?

I have three stringers on decking stairs that go from the yard to the second story, and all three are showing signs of rot with two showing decent rot in at least 3 places. It's easily over 8 feet from the yard to the deck (11 stairs). To be honest, the entire deck needs to be replaced as it's probably 20-25 years old and wasn't maintained in the years prior to when we bought the house. However, I don't have the money right now to completely replace the deck. The stringers are the main piece that's failing. The deck doesn't get heavy use anyway - the dog uses the steps more then us and we don't have any kids. Instead of ripping out all three stringers and the steps, I'm wondering if I can simply sister 3 new stringers to hold off on needing to rip the entire stairs down? My thought process is outside of the spots that are showing rot, the other areas of the stringers are solid so it should hold.