Difference between ない（もの）でもない and なくはない・なくもない


I would like to know if both structures ない（もの）でもない and なくはない・なくもない are
completely interchangeable or if there is any difference between them. It
seems that both of them have the same meanings (1: it is not that ... / 2:
may, might). However, whereas in some textbooks like Nihongo Sou Matome N1 and
some websites like, for example, this one

<https://nihongokyoshi-net.com/2019/06/10/jlptn2-grammar-naidemonai/>

<https://nihongokyoshi-net.com/2019/06/17/jlptn1-grammar-nakumonai/>

ない（もの）でもない and なくはない・なくもない are treated separately (in spite of no apparent
difference in meaning), in some other textbooks like Try N1 and other grammar
websites, ない（もの）でもない and なくはない・なくもない are included in just one grammar point.

Therefore, if possible, I would like to know if they actually have any
difference, and in case there is, to see an example where they are not
interchangeable.


  
  
The role of this も has been discussed in this site several times. Basically
it's a softener.

  * [Meaning of く も in this sentence](https://japanese.stackexchange.com/q/65646/5010)
  * [Usage of も in そんなこともないけど](https://japanese.stackexchange.com/q/51841/5010)
  * [What is the difference between 「とは限らない」and 「とも限らない」](https://japanese.stackexchange.com/q/55266/5010)
  * [も in 「Vのもアレなんだけど」](https://japanese.stackexchange.com/q/55970/5010)

Then what's the difference between ないではない and なくはない (or the difference between
ないでもない and なくもない)? The difference is very small, but ないではない /ないでもない sounds a
little more formal or literary to me. なくはない/なくもない is more common in casual
conversations (especially among children).


  
  
The role of this も has been discussed in this site several times. Basically
it's a softener.

  * [Meaning of く も in this sentence](https://japanese.stackexchange.com/q/65646/5010)
  * [Usage of も in そんなこともないけど](https://japanese.stackexchange.com/q/51841/5010)
  * [What is the difference between 「とは限らない」and 「とも限らない」](https://japanese.stackexchange.com/q/55266/5010)
  * [も in 「Vのもアレなんだけど」](https://japanese.stackexchange.com/q/55970/5010)

Then what's the difference between ないではない and なくはない (or the difference between
ないでもない and なくもない)? The difference is very small, but ないではない /ないでもない sounds a
little more formal or literary to me. なくはない/なくもない is more common in casual
conversations (especially among children).

