I went over to the next block to speak with a complainant. She mentioned there was defecation on the stairwell - and indeed there was.
The complainant asked me in for a drink and explained that she was not against the cat, but that she was getting quite tired of cleaning up. This was especially as she was heavily pregnant or she would clean up the area. I took a photo of this cat which was sitting one landing above hers, and she said that she could not be sure it was this particular cat defecating (and she didn't want to accuse the wrong cat) but she saw this cat around very often.
Quite a few other neighbours confirmed this. This cat was extremely friendly and followed me around as I was walking up and down.
Two different neighbours confirmed the cat belonged to or was cared for by a family. When I approached them, they denied it vehemently. The neighbour below them though, identified the cat as theirs. She said it ran into her house sometimes and she would go upstairs and return the cat to them. She was quick to add this didn't happen often, and I don't think she had a problem with it.