Since we can use multiple negatives in French, is there an order that they should be in when more than one is used, e.g. is it more correct to say "Je ne connais plus personne," or "Je ne connais personne plus," or are they equally correct (with possibly a difference in meaning)?
Plus pas, aucun plus, rien plus, personne plus are impossible so only the first form is correct:
Je ne connais plus personne.
Same for rien:
Il n'y a plus rien.
With jamais, both orders are possible but the meaning can be different :
Plus jamais ça ! = Jamais plus ça ! The latter is slightly more literary.
Different meanings possible:
il n'est plus jamais fatigué ≠ il n'est jamais plus fatigué (que lorsqu'il il ne dort pas assez)
The second sentence might be ambiguous without context because plus can be either positive or négative.
There is the same kind of ambiguity with plus and aucun:
Plus aucun ne parle is unambiguous: no one is speaking any longer.
Aucun ne parle plus is ambiguous, either same meaning as the previous sentence or the opposite: "no one stays mute".
Guère plus and plus guère have different meanings and again, plus is positive when not in the first position:
Il n'y a guère plus de dix habitants ici. There is just over than ten inhabitants here.
Il n'y a plus guère d'habitants ici. Not much people still live here.
Plus is always positive in the sequence pas plus:
Je n'en veux pas plus. I don't want more of it.