We have an eight year old Tortoiseshell housecat (not through choice, she was already a housecat when we got her) whom we got from a rescue centre about a year ago.
She is a lovely cat and is very gentle and sweet, but has 'Tortitude' in buckets, very vocal, very demanding and wants constant attention. If you stop stroking her she will meow until you start again. Imagine if you can Mariah Carey in cat form.
As we are out during the day, we are beginning to worry that she gets lonely and bored without us and may benefit from another cat to provide a bit of company for her. Equally we would worry that she might feel put out and resent another cat encroaching onto her territory. The last thing we would want to do is upset her now she has a settled home with us.
It's a difficult one and really you can't know unless you try. In my experience most cats in that position will eventually accept and even become close to another cat being brought into the home, but it can often take quite a few weeks. And a small minority never accept the other one and at best come to some sort of truce.
The rescue centre should be able to tell you which cats like other cats, so that will help, but you can't know how yours will react. Of course all rescue centres will take back any cat they rehome if it really doesn't work out, but you may need to give it at least two months.
In fact I met a couple last week who had had a flat cat for 15 years and then decided to introduce a new young cat. They said that the old cat was quite wary at first, but soon calmed down. And I took the young cat away to be neutered for them and when I brought her back they said that the old cat had spent the whole day wandering round the flat looking for her and crying. So they had obviously become close.