Here we will introduce you the Extreme Stone in Last Chaos. Have a look. An ES can be purchased from the IM with AP, can be purchased from another player or the Merchant Mart with in-game gold, or can be purchased with Reputation Points from Magical Shopkeeper Coen in the town of Randol. An ES also can only be used once on any item, if an item was ever plused with an ES, and later downgraded to +10, an ES can never be used on that item again. Will not work on any gear that is level 146 or above.
Do not expect this to be a prize from any event, the possibility is not non-existant, but it is highly unlikely. An ES guarantees an upgrade of +1 to any item(last chaos gold) that is +13 or lower. It is unwise to use an ES on any item that is not at least +12 already. It will not make a +14 into a +15.
There is no need to use any RoP with an ES. If you want to make the item into +15, you should use the ES when the item is +13. If you are willing to settle for a +13 item, use the ES when the item is +12, but be aware that such an item will not be worth as much gold as a +13, which has not had an ES used on it if you elect to sell the item. Also here is the cheapest last chaos gold service.
You may then use Platinum Refining Stones, available from the IM or from other players or the Merchant Mart, which will add a +1, +2, or +3, but only for 24 real-time hours, or use Bonus Books of Melding, available from the IM, or from other players or the Merchant Mart; note that once opened, a Bonus Book of Melding cannot be bought/sold by players or put into or bought from the Merchant Mart, and a weapon cover or armor covers which are ordinarily only available from the IM, but there are some events which grant them to get the item a plus that lasts for 30 real-time days.
