I think introducing another cat can be beneficial but it can certainly depend on the relationship between the previous two cats and the type of personality of the next one you bring in. I've had varied results with having to go through this situation twice in the last 18 years. My first two that I had were extremely close. As one as died and I've introduced a new member to the house, those two in turn have never had that same type of close relationship unfortunately.

It probably depends on how well the new one can adapt in w/the old and if they're used to sharing their "person". My new guy is pretty territorial w/me and attacks the other. She in turn won't let him w/in 2 ft of her.

As someone else said, time may help heal this as your cat gets used to being alone. But if you're like a lot of cat people, one cat just isn't enough. Good luck w/whatever you decide.