School

OG Parasect had three x4 weaknesses due to the Gen 1 Type chart. It still retains two of them in Fire + Flying but the other was Poison back in Gen 1(Poison was weak to Bug at the time too). The only way to get three x4 weaknesses today is if a Pokemon is hit with a move like Forest Curse and gains a 3rd typing that when combined with its other typings results in additional x4 weakness. Nincada, for example, is Bug/Ground and if hit with Forest Curse would make it Bug/Ground/Grass, giving it Flying(x4), Fire(x4) and Ice(x4) weaknesses.

Similarly, using Soak to add Water typing could result in x4 but whether it yields three x4 I haven't looked into.