I have found multiple threads about how the Necklace of Ki Serenity interacts with Quigong Monks, but I have not found many (maybe none I cant say for sure). That talked about how it ineracted with Unchained Monks and Ki Powers.
The Necklace says:
This simple leather cord is tightly knotted at even intervals and gives its wearer a sense of inner calmness and connection with the larger world.
The wearer gains a +4 bonus to his effective level when determining the size of his ki pool and the level-based effects of his ki pool ability (such as bypassing damage reduction).
For Vanilla monks, it would definitely stop right with the bonuses described in the Ki Pool skill, but for Unchained Monks the Ki Pool Skill mentions the abilities gained later.
At 3rd level, a monk gains a pool of ki points, supernatural energy he can use to accomplish amazing feats. The number of points in a monk’s ki pool is equal to 1/2 his monk level + his Wisdom modifier. As long as he has at least 1 point in his ki pool, he can make a ki strike.
At 3rd level, ki strike allows his unarmed attacks to be treated as magic weapons for the purpose of overcoming damage reduction.
At 7th level, his unarmed attacks are also treated as cold iron and silver for the purpose of overcoming damage reduction.
At 10th level, his unarmed attacks are also treated as lawful weapons for the purpose of overcoming damage reduction.
At 16th level, his unarmed attacks are treated as adamantine weapons for the purpose of overcoming damage reduction and bypassing hardness.
By spending 1 point from his ki pool as a swift action, a monk can make one additional unarmed strike at his highest attack bonus when making a flurry of blows attack. This bonus attack stacks with all bonus attacks gained from flurry of blows, as well as those from haste and similar effects. A monk gains additional powers that consume points from his ki pool as he gains levels.
The ki pool is replenished each morning after 8 hours of rest or meditation; these hours do not need to be consecutive.
Probably grasping at straws here, but since the ability mentions later powers does that mean the Necklace affect those later powers that are based on monk level?
You are grasping at straws. "Level-based effects of his ki pool ability (such as bypassing damage reduction)" is pretty clear that the necklace does not extend to other monk ki powers, just those specifically stated that he gets from the ki pool class feature, such as DR bypassing and his additional attack.
Largely expected as much, but I figured it couldn't hurt to see if someone had already questioned it.