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Supposing, as a monk, I come into vast amounts of money and, heh, lack the wisdom to spend it otherwise...
If I have both a Body-Wrap of Mighty Fists and an Amulet of Mighty Fists, both enchanted to their maximum of +7 and +5 respectively, do the effects of both items, presuming they are otherwise compatible effects, stack together to give me an effective enhancement bonus of +12 to my unarmed attacks?

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The maximum effective enhancement bonus a creature can have on its unarmed strike is +10, but discuss with the GM changing that in this case

Unlike its predecessor D&D 3.5, Pathfinder on Magic Weapons says

Some magic weapons have special abilities. Special abilities count as additional bonuses for determining the market value of the item, but do not modify attack or damage bonuses (except where specifically noted). A single weapon cannot have a modified bonus (enhancement bonus plus special ability bonus equivalents, including those from character abilities and spells) higher than +10. A weapon with a special ability must also have at least a +1 enhancement bonus. Weapons cannot possess the same special ability more than once.

(Emphasis mine.) Thus, despite its quirks, like any other lone weapon, a monk's unarmed strike is limited in the manner described above. The player of a monk that activates a body wrap of mighty strikes that possesses a total of a +7 enhancement bonus in appropriate magic weapon special abilities while wearing a +1 amulet of mighty fists that possesses a total of a +4 enhancement bonus of appropriate magic weapon special abilities must discuss with the GM which of the wrap's magic weapon special abilities activate and which don't so that the total doesn't exceed an effective +10 enhancement bonus on the monk's unarmed strike.

However, this reader thinks parts of this rule are terrible, and this GM ignores the parenthetical including those from character abilities and spells (that, by the way, goes largely unmentioned elsewhere as can be seen by questions here and here). Further, this GM assesses the quoted passage wholly in context so that it applies only to specific magic weapons like a +5 vorpal scimitar rather than having the rule cascade throughout the game to affect, for example, an otherwise nonmagical weapon on which has been cast a crapton of spells that buff it and wondrous items that happen to affect weapons like the amulet and the wrap. My campaigns have benefited rather than suffered because of this GM's more liberal stance regarding this loathsome and oft-overlooked rule.

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    \$\begingroup\$ To summarise for clarity's sake: by the RAW this is a no-go and the situation creates a messy debate over where the lost +2 comes from, and by GM-fiat it seems reasonable and is worth discussing. \$\endgroup\$ – royalmurder Apr 26 '18 at 15:57
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    \$\begingroup\$ @royalmurder Yep. That's pretty much it. (Personally, I'm of the opinion that some of Pathfinder's changes from 3.5 were made without consulting the source in context, and this is an example of that. As the linked 3.5 question shows, this is a Pathfinder-exclusive quirk that could've been easily and accidentally implemented by a designer who thought the less clear and without context SRD needed to be brought up to code.) \$\endgroup\$ – Hey I Can Chan Apr 26 '18 at 16:08

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