Question
The item must have exactly the correct number of sockets to trigger a Runeword.
Is there a way to add multiple sockets or even remove multiple sockets?
Answer
No
There are two main ways to socket white items: the Horodric cube, and Larzuk. Both require unsocketed items. The Horodric Cube recipes only work for non-superior items, which makes superior items with less than max sockets valuable, if they have the correct number for a popular item.
Socketing Items at Larzuk
Larzuk is occasionally, if infrequently, a good choice for socketing a white item. He'll give it the maximum number of sockets it can have, which depends on item type and item level (which is hidden, but can be inferred if you know what monster dropped the item).
The usefulness of that is limited, since you can only socket three items per character at Larzuk (one per difficulty as a quest reward), and it's more common for items to need less than max sockets to reach their true potential: 3 socket armor is much more valuable than four socket armor, because most of the good armor rune words use 3 sockets, and four sockets is much easier to find.
Larzuk is the only way to add sockets to superior white items, however, so there are a few cases when it's worthwhile to spend your Larzuk socket on a white item, instead of saving it for an otherwise unsocketable set or unique item.
Horodric Cube Socketing Recipies for White Items
These work only for non-superior, non-low-quality white items.
1 Tal Rune + 1 Thul Rune + 1 Perfect Topaz + Normal Body Armor
=> Socketed Body Armor of same type1 Ral Rune + 1 Amn Rune + 1 Perfect Amethyst + Normal Weapon
=> Socketed Weapon of same type1 Ral Rune + 1 Thul Rune + 1 Perfect Sapphire + Normal Helm
=> Socketed Helm of same type1 Tal Rune + 1 Amn Rune + 1 Perfect Ruby + Normal Shield
=> Socketed Shield of same type
The number of sockets is chosen randomly between 1 and the max for the item type (4 for body armor, 6 for weapons, 3 for helms, 4 for shields), and then capped at the max for the specific item, based on type and ilvl.
So, for example, a crystal sword dropped in Normal difficulty act 5, capped at 3 sockets by ilvl, will get three sockets 4/6ths of the time, two sockets 1/6th of the time, and 1 socket 1/6th of the tie, while a high level circlet will get one, two or three sockets with equal probability, because the maximum number of sockets for a helm is 3, while the maximum number of sockets for a weapon is 6.
source: Arreat Summit: Horodric Cube
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