as no one has risen to the challenge yet (and I do have a reputation to maintain ;), here are some useless words which have *more than* three...

epigaeous - growing on, or close to, the ground
maieutic - relating to or resembling the Socratic method of eliciting new ideas from another
eugeuia - allspice and clove producing plants
plateauing

oh, and I just noticed that you have onomatopoeia on your list, and in that vein:
mythopoeia pharmacopoeia prosopopoeia

and now, just to start a fight, I present you with
blueeyed (5?)
yo-yo (all 4?)