You can't add a landing. You might could build the stairway entirely, but that would be big bucks, and require you to take up more living space for the expanded steps. This would have to be done to code too.

You could add a handrail on the other side. Carpet on the treads might help (until it gets in rough shape, when it could become a bigger hazard than just a wood tread).

The safest thing for older family members is to move them upstairs and for you (or some younger members of the family) to move downstairs.

How much is your budget for this project? If it's $$$ - you could have the staircase rebuilt entirely in order to add a landing + other safety options.

What exactly do you mean by "older family members?" Depending upon your age/perspective, "older" might = 60/65/70/75/80/etc. Also, age doesn't tell the whole story. My SO's mom is 90 - and she has less health/mobility issues than my dad did when he was 72-74 (he had congestive heart failure + Parkinson's). My SO's mom (she's basically my MIL - we've been together for a long time) still lives in the split level house where my SO was raised (for most of his life). She has some issues with arthritis in her knees - but she handles the stairs fine on a daily basis (kitchen is on the main floor - with the formal living room - however, she uses the family room that is down a level + her bedroom is upstairs).

She does use a cane to help steady herself a bit at times - but she can get around safely - and I cannot imagine her deciding to leave that house (unless there is a major change).

My nana was the same way - she stayed in her home until she was just shy of 90 - used two full sets of stairs every day. The only reason she left her home was so she could move to the city where my mom (we) lived (she had started to have some dementia issues - and my mom convinced her that it was "our turn" to have her live near us "temporarily"). My mom assured her that her house would still be there when she was ready to return to Chicago after spending time with her grandkids and great grandkids (her house wasn't sold until after she passed away a few years later).

My point is - unless you share a little bit of information in order for others to have be able to have a bit of an understanding about the situation, it is difficult to offer suggestions/advice regarding such an important topic.

You could find an unused closet - and add an elevator! My understanding is that residential elevators have become more common than they used to be.

OR - the "youngsters" could trade places with the "older family members" as suggested above (although I would still make a few simple updates to the staircase in order to increase it's safety aspect).

Can you cut any of that wall where the railing currently resides. If you can, then maybe a landing can be created.

Start by switching the basement door swing, so it opens into the room, not over the stairs.

Steep staircases are unsafe, period. My elderly , seemingly fit tennis playing neighbor 80+ fell down his & died, very sad. Another person I know, 61 years young ( to me ), fell down stairs at a vacation cabin, severed his brain stem, same terrible result.