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Tentative attunement rules:
Version A: BIGGER POCKETS:
instead of a limit of 3 magic items, a character can attune to a maximum number of items equal to their proficiency bonus +1. Attunement otherwise follows standard rules.

Version B:
No limit on attunable items, but attuning takes more time. Instead of simply counting items, each magical item that would require attunement is assigned an attunement progress clock. In order to attune to an item a player must fill that progress clock over time. The size of the progress clock is based on rarity, with common items requiring 1 success, uncommon 2, rare 4, very rare 8, and legendary 16. Sometimes, an intelligent, cursed, or personally relevant item may start you off with free progress.

1. Attunement points are earned by focusing on the magic item over the course of a rest. During a short rest, a player may roll a single d20 against the attunement DC of an item; four rolls may be attempted during a long rest. Critical successes count for double, while critical failures subtract progress. You may forego the benefits of this rest retroactively to add your proficiency bonus to the rolls, or decide at the start of the rest to gain advantage as well as adding your proficiency bonus.
2. Attunement points are also earned by sacrificing completed attunement clocks on other items during a short rest. For example, if Marjoram has already attuned to an item with a clock totaling 4 segments, but doesn't want to spend all the time necessary to attune to an item requiring 8, he may lose the benefits of the previous item to instantly progress partway to the new item. This exchange does not give you your "change"; sacrificing attunement to an 8-segment item might fill up 4 segments on a new item, but the difference would not pass to a third item. If the new item is very rare or legendary, the character must succeed a roll against the new item's attunement DC or only transfer half of the progress sacrificed.
3. Characters have a pool of "free" attunement points equal to their level. When the total attunement of all your desired items is less than your level, you can effectively ignore this ruleset.
     
 
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