Here is a quote from a famous paper by Geoffrey K. Pullum, Syncategorematicity and English infinitival to:
[A]lthough not can follow a finite auxiliary that is stranded by VP ellipsis, it is impossible to have not after a stranded nonfinite auxiliary. (Pullum 1982: 201–202)
Pullum's observation describes the following kind of data:
- Bob is attending but Ben is not.
- *Bob is attending but Ben might be not. (ungrammatical)
- Bob is attending but Ben might not be.
- Bob is attending but Ben might not.
In (1) we can see that the non-finite verb phrase attending has been ellipted from the clause in the second coordinate, Ben is not [
attending]. The word not here follows the tensed auxiliary (and therefore finite verb form) is. This sentence is therefore grammatical because not is following a finite verb form.
However, in sentence (2), the phrase after not has been ellipted, but the verb before not is the non-finite plain form of the verb BE. This verb has no tense and is therefore non-finite. This sentence is therefore not grammatical.
In example (3) where not precedes the non-finite verb form be instead of following it, the sentence is fully grammatical.
In (4) we see the word not preceding the ellipsis. However it occurs directly after the finite auxiliary verb might. So sentence (4) is also grammatical.
The Original Poster's example
*It may be not [
like that]. (ungrammatical)
It may not be [
In (5) the word not directly precedes the ellipsis site. However, the word not itself is preceded by the non-finite verb form be. It is therefore ungrammatical. In (6), however, the word not occurs before the verb and not before the ellipsis site. (6) is therefore perfectly fine.
Note for grammar junkies
One might wonder why this particular piece of data is so important. Well, in grammars such as The Cambridge Grammar of the English Language it is argued that infinitival to is a subordinator. However, there is also a very compelling argument that the word to is non-finite auxiliary verb (yes, a radical idea). One piece of evidence that this is the case is that not cannot precede an ellipsis site when it directly follows the word to. In other words, to patterns in this respect like the non-finite auxiliary forms of be above:
- *Bob wants to go there but Bill wants to not. (ungrammatical)
- Bob wants to go there but Bill wants not to.
For further arguments explaining why to is probably a non-finite auxiliary verb see this paper by Robert Levine, 2012, Auxiliaries: TO's company.