It could also be that your kitty needs more than one litterbox - my Weeble
likes to poop in one & pee in the other.  Try another litterbox.

Perhaps you should seek another opinion. Peeing outside the box can be the
result of medical problems.

Couple of things.  First, the cats could be coming by at night and
marking so she doesn't really "see" them, she smells them.  I've
never heard of a female marking territory like a male but then I
never heard of a lot of stuff so that doesn't mean it doesn't happen :-)

Secondly, my experience has been that my cat would pee in the sink
or tub when she had a urinary tract infection.  If you have complete
confidence in this vet and he really checked her out than try a second
box as others suggested.  If not, you may want to first make sure
it's not medical.

Single cats do exists...I have one.  Most will learn to tolerate another cat
if introduced properly but they are happy being alone too and if you
do get another cat, you either have to get two others or you have to get
another cat that will only tolerate yours.  Not fair to get a cat that wants
a playmate when yours doesn't want to be one.  Sasha has given me
a couple of clues.  The rescue group of course warned me but also
she had 0 interest in the mom cat I fostered.  I even introduced her to
the babies thinking I might adopt one but a first she just ran the other
way and then she feigned indifference.  I tried later with a kitten that
was about 8 weeks old.  I probably should have introduced them more
slowly but even after she stopped hissing at him, she didn't want to be
around
him.  If he came into a room, she would leave.  If he jumped on the bed,
she would jump down. If he approached her when she was sleeping, she
would smack him then walk away.  I ended up giving him to a family with
a mom cat that had just lost her kitten.  He's in heaven, Sasha is 100% more
content and I am back to just 2 litter boxes.  I'd say alls well that ends
well
but I did miss the little guy.  Anyway, how does your cat act around other
cats?  A lot of them will fight at first but if they are indifferent or
"bothered"
than I'd say you have an alone cat.

AG

 You did not mention if you had cat actually to the vets - may want to have
them check for diabetes, kidney or liver disease as well as UTI.  Is she
fixed?  If not, females going in to heat have been known to mark their
territory, the mother I was fostering did it once, once she got fixed the
issue went away.

 Try the above and try adding an extra pan.

 >     I have a cat that for about the last 3 weeks now, has been pooping
 > normally in the litterbox, but she now pees anywhere but in the
litterbox.
 > My vet says my female kitty is probably seeing other cats and is marking
 > her territory.  Well, she can only see in the back & side yards and
there
 > are no stray cats out there (I have never seen any in 1+ year).
 >
 >     Does this mean that my kitty will never be able to get along w/
other
 > cats?  Like how you see ads in the classifieds, how can they tell if a
cat
 > will only be happy as the only cat in the household?  Do you think mine
is
 > one of those?
 >
 > --
 > "Expect nothing.  Live frugally on surprise." -- Alice Walker

I have a similar experience. I have a 2-year-old cat, Pickles, who is
extremely fastidious with his litter box: the box must be cleaned very
thoroughly and if I was a millionaire, the entire cat litter changed
afresh each time my cat uses his box. There was a time when I had lots
of problems with him; he would poop on my couch but not in his litter
box (though still clean). He also ventured out late into the night and
I spend many nights waiting for him to come back so I could sleep!

However, when I got him Pumpernickel, a female kitten/companion,
things improved though not at first. There was the usual hissing
between the two and Pickles would pounce on Pumpernickel just to show
her who is boss. It was like that for a month or two, but then I
started to notice that Pickles has stopped pooping on my couch and
would stay nearer my house and wander less. Both of them now get along
very well and love playing hide-and-seek games.

Overall, getting Pickles a companion has solved some big problems I
had. I hope this helps.