Can a weapon that provides bludgeon damage administer Poison

i wouldn't allow a poison to be applied in layer to affect a target multiple time over a single hit, based on the concept of Combining Game Effects.

I wouldn't even allow different poisons to be applied to the same weapon, limiting weapon or ammunition to 1 coating at a time.

Combining Game Effect: Different game features can affect a target at the same time. But when two or more game features have the same name, only the effects of one of them—the most potent one—apply while the durations of the effects overlap. For example, if a target is ignited by a fire elemental’s Fire Form trait, the ongoing fire damage doesn’t increase if the burning target is subjected to that trait again. Game features include spells, class features, feats, racial traits, monster abilities, and magic items. See the related rule in the “Combining Magical Effects” section of chapter 10 in the Player’s Handbook.

As for 5.5E rules specifically phohibiting it, i'm not sure there's any. Poison in the DMG doesn't address it and the core rules only has rules against Combining Spell Effects, which exclude Poison. 

Something in the rules a DM could use to shut this down could be on principles for Players Exploiting the Rules;

Rules Rely on Good-Faith Interpretation. The rules assume that everyone reading and interpreting the rules has the interests of the group’s fun at heart and is reading the rules in that light.

Outlining these principles can help hold players’ exploits at bay. If a player persistently tries to twist the rules of the game, have a conversation with that player outside the game and ask them to stop.

Might fall under the duplicate effects rule. Similar to multiple spells of same name. Or the ruling that most people make with multiple flasks of oil.

Quote from TarodNet >>

Random thought. Not something I'd allow in my games, but Injury says:

Injury poison can be applied as a Bonus Action to a weapon, a piece of ammunition, or similar object.

RAW, could you apply, for example, the Serpent Venom poison multiple times to the same weapon? Or is there any rule I'm missing?

 Are you asking if you can apply multiple instances of the poison to one weapon for a single attack? Or applying it in different rounds?

I would say you cannot apply it, say, 3 times to a weapon and then attack for an extra 9d6 damage (assuming they fail 3 saving throws). It simply says "a creature subjected to the poison", so I would say the amount on the blade doesn't matter. It does the same damage if you dip the point of a throwing dart in the poison as it would if you coated an entire great sword blade in it.

But can you apply it round after round if you have enough of it? RAW it seems so. It doesn't provide a lasting effect, only extra damage. There's nothing in the description that suggests that you automatically succeed on saving throws against it or are immune to it after you've been subjected to it (something like the language from saving throws against certain charm effects from various monsters). If you have a supply of 5 uses of the poison then I would think you could apply them with your bonus action before each new attack and do 15d6 worth of poison damage if they fail all the saving throws. You're using your action economy resources, as well as disposable resources, to do it. 

I would assume in-game something like this might be hard to come by.

Quote from Plaguescarred >>

i wouldn't allow a poison to be applied in layer to affect a target multiple time over a single hit, based on the concept of Combining Game Effects.

I wouldn't even allow different poisons to be applied to the same weapon, limiting weapon or ammunition to 1 coating at a time.

Combining Game Effect: Different game features can affect a target at the same time. But when two or more game features have the same name, only the effects of one of them—the most potent one—apply while the durations of the effects overlap. For example, if a target is ignited by a fire elemental’s Fire Form trait, the ongoing fire damage doesn’t increase if the burning target is subjected to that trait again. Game features include spells, class features, feats, racial traits, monster abilities, and magic items. See the related rule in the “Combining Magical Effects” section of chapter 10 in the Player’s Handbook.

 As I said, it's my ruling too, so I agree.

IMO, the 5e DMG is still valid for 5.5e, especially for DMs, obviously, but as we commented in 2024 DMG: Combining Game Effects, that rule is not in the new books.

EDIT: well, you've also mentioned that :)

Quote from MaximusArael020>>

Quote from TarodNet>>

Random thought. Not something I'd allow in my games, but Injury says:

Injury poison can be applied as a Bonus Action to a weapon, a piece of ammunition, or similar object.

RAW, could you apply, for example, the Serpent Venom poison multiple times to the same weapon? Or is there any rule I'm missing?

 Are you asking if you can apply multiple instances of the poison to one weapon for a single attack? Or applying it in different rounds? [...]

 "multiple instances of the poison to one weapon for a single attack", yes, sorry for not being clear.

I agree with your answer.