As a previous owner 6 cats (sadly I am down to 5) and having dealt w/ older cats that don't want to get in the box....I second much of the advise and have a bit more....
Is the present pee or poop?
Peeing is a big issue. And I have used the Feliway---we spray it IN the box. It has helped.
I second the removing of covers. In my expeirnece the older or more quiet cat will feel "cornered" and I have even witness "corning" of the older cat by the others. They think it is fun...she did not! So no covers on any box any more.
Not sure what litter you use...found the good, old fashioned clay (not scoopable) is often their favorite...so keep one litter box w/ just that.
Move the new extraa litter box away from the others. So that one could become hers.
At one time we have 5 litter boxes for 6 cats.
We are down to 2 inside and one outside on screen porch for 5 cats.
But we scoop every AM and PM. They all want a fresh box. Believe it or not you can even "scoop" pee in clay litter--just takes a bit of practice.

My oldest female even now will get "cornered" in the box. It is like she has "victim" stamped on her forehead. And when she was younger she did this to her older sister!! So what goes around comes around.
My problem w/her is that she sometimes does not get her butt in the box and therefore pee's just outside of the box. (Did this last night, right in front of me when I got home from dinner )

Good luck. Just keep trying.

K