I tried it after equiping a neckpiece, a glove and a ring with 'Fortify Smithing' enchantment and I could upgrade it once more but after that I couldn't upgrade it anymore.
You can also put Fortify Smithing on any piece of apparel for the torso: robes, apron, armor, etc. That would give you a fourth buff instead of just three. Drinking a Fortify Smithing potion while wearing the enchanted gear will provide an additional buff. Equipping the Notched Pickaxe if you have it will give you yet another buff.
As has already been noted, once you have improved something you cannot improve it any further unless your skill increases by the amount necessary to get an additional improvement. If you are already at 100 in Smithing with the necessary perk, the only way to increase your skill is to keep adding additional buffs that stack with each other via enchanted gear and potions, or to sub in new gear/potions that provide a total buff that is more than what you had on the previous trip to the grindstone and also a big enough increase to let you improve the weapon further.