François is partially right, you will have to learn by heart when to pronounce the "s" or not with set phrases. But it has nothing to do with subjects or verbs, There is one little trick when "plus" is used by itself (so not in a set phrase). When "plus" gets the sense of "anymore", you pronounce it [ply] without exception. -Il n'est plus là. He isn't here anymore. -Je n'ai plus de maison. I don't have a house anymore. -Je ne vais plus à l'école. I don't go to school anymore. Let's have a look at these sentences which can mean two things depending on how you pronounce the "plus": 1. J'en veux plus. [ply] > I don't want it anymore. (This is informal, in formal language you'd say Je n'en veux plus) [plys] > I want more of that. 2. Plus que toi. [ply] > You're the only one left. [plys] > More than you. It can be very confusing, but you just have to get used to it...

Well the more often it is with the s prononciation . When it is not said it is mainly because there is a subject or a verb after. But I am not quiet sure about this rules works in anycase

Pour les expressions en question, voici les bonnes prononciations : de plus, pas plus [plys] non plus, ne plus [ply] il y a plus => dépend de la phrase, voir la réponse de Hyejeong.