How sexual relations with multiple partners affect us? What are after effects of promiscuity? I want to know how promiscuity affects us? How it binds? What are the after affects of making many sexual partners?
In his 1st sermon, the Lord Buddha taught: 


  Now this, bhikkhus, is the noble truth of the origin of suffering: it is this craving which leads to renewed existence, accompanied by
  delight and lust, seeking delight here and there; that is, craving
  for sensual pleasures, craving for existence, craving for
  extermination.


Therefore, the more sexual partners, which is interactions based on lust, the more suffering. 

Buddhism teaches to relate to people with non-harming (ahimsa), loving-kindness (metta) &amp; compassion (karuna). Therefore, there is absolutely no place in Buddhism for the recommendation or endorsement of sexual promiscuity, because sexual promiscuity is a behaviour (kamma) rooted in lust. 

MN 9, which is about Right View, states: 


  And what is the root of the unwholesome? Greed (lust) is a root of the unwholesome; hate is a root of the unwholesome; delusion is a root
  of the unwholesome. This is called the root of the unwholesome.


The Dhammapada states: 


  Verse 202: There is no fire like lust.


In Buddhism, if a person needs to have sex due to strong natural urges, a person should establish a relationship based on loving-kindness &amp; compassion. 

In the Pali suttas, there are no teachings about how to engage in sex because all of the teachings are about how husbands &amp; wives should behave in the more important compassionate &amp; loving ways. For example, in AN 4.55, it is taught when a husband &amp; wife are complete with virtue &amp; love towards each other, they will naturally enjoy whatever sexual pleasures they desire. 

In conclusion, Buddhism describes the world of promiscuity as the 'animal world', as follows: 


  ... the world would have fallen into promiscuity, as with goats, sheep, chickens, pigs, dogs, and jackals. AN 2.9


Therefore, Buddhists that tell other people that sexual promiscuity is "OK" are teaching the path (magga) leading to animal birth (tiracchā­na­-yoni-­gamanīyā), as follows:


  And what is the cause of defilements? Ignorance is the cause of defilements.
  
  And what is the diversity in defilements? There are defilements that lead to hell, those that lead to the animal womb (tiracchā­na­yoni­gamanīyā), those that lead to
  the realm of the hungry shades, those that lead to the human world,
  those that lead to the world of the devas. This is called the
  diversity in defilements.
  
  And what is the cause of kamma? Contact is the cause of kamma.
  
  And what is the diversity in kamma? There is kamma to be experienced in hell, kamma to be experienced in the realm of common animals (tiracchā­na­yoni­ve­danīyaṃ), kamma
  to be experienced in the realm of the hungry shades, kamma to be
  experienced in the human world, kamma to be experienced in the world
  of the devas. This is called the diversity in kamma.
  
  https://suttacentral.net/en/an6.63