Why do Buddhists argue that nirvana is nothing in addition to the skandhas? Why do Buddhists argue that nirvana is nothing in addition to the skandhas? I found this, and I hope it suffices to demonstrate that's what the Buddha taught:


  "What do you think: Do you regard the Tathagata as being in
  form?... Elsewhere than form?... In feeling?... Elsewhere than
  feeling?... In perception?... Elsewhere than perception?... In
  fabrications?... Elsewhere than fabrications?... In consciousness?...
  Elsewhere than consciousness?"
  
  "No, my friend."
  
  "What do you think: Do you regard the Tathagata as
  form-feeling-perception-fabrications-consciousness?"
  
  "No, my friend."
  
  "Do you regard the Tathagata as that which is without form, without
  feeling, without perception, without fabrications, without
  consciousness?"
  
  "No, my friend."
  
  "And so, my friend Yamaka — when you can't pin down the Tathagata as a
  truth or reality even in the present life — is it proper for you to
  declare, 'As I understand the Teaching explained by the Blessed One, a
  monk with no more effluents, on the break-up of the body, is
  annihilated, perishes, &amp; does not exist after death'?"


The quote seems to say that the Tathagata is not without form feeling etc.. 

If nirvana were something in addition to the aggregates, then I'm thinking the Tathagata would be without the aggregates. On the grounds that nirvana is all that the Tathagata is.
In the Yamaka Sutta, Ven. Sariputta, made Yamaka to understand that the five skandas are anicca. If one truly understands this reality the extinction of the process happens in the form of ‘Nibbana’.   If we willingly attach to these five skandas with the nicca sanna, then we suffer. Only in realizing that nothing can be maintained to one’s satisfaction in the long run, can we arrive at Nibbana. 

Nibbana is not sunnata or emptiness. The person who attained Nibbana is only empty of the five upadanaskandas. The five skandas remain. It is like this. if we take a water bottle and pour the water out, we say we have an empty bottle. But in reality there is air in the bottle, so the bottle is empty only with regard to water; it is not empty regard to air. 

Thus what is meant was that “it is empty of”. There is no absolute “emptiness”. At Nibbana  one is empty of greed (raga), hate (dosa), and ignorance (moha). At Arahanthood, even the slightest bondage to anything material is discarded.  

For one who has attained Nibbana, there is only "ditthē dittha mattan bhavissati- sutē suta mattan bhavissati- mutē muta mattan bhavissati” – There is only seeing in the ‘seeing’; only hearing in the ‘hearing’ etc. It is only you and I, that take nimithi &amp; anu nimithi  (impressions of objects) from what we hear or see.

As long as there is greed, ill will &amp; delusion we retain impressions of objects (nimithi anu nimithi) of self &amp; pleasurable things. The impressions stimulate our senses and thus we see people &amp; things around us. Only the minds that are polluted with greed, hatred &amp; delusion associate four elements. The one who sees arising ceasing nature of aggregates sees the emptiness of any inherent meaning &amp; will not retain impressions thereby abandoning the defilements of greed hatred and delusion.