Spells with ongoing effects of the same type cannot affect a creature twice. Poisons are not spells. That being said, you also can’t get the poisoned condition twice, and the poisoned condition underlies most ongoing poison effects. This is a double-edged sword though: If DMs rule this way, they should prepare for players to have their characters get drunk before battles with venomous creatures, so that they won't be affected by the creature’s poisoned condition effects.