There's nothing per se "wrong" syntactically with double or multiple negation. In principle, the following sentence is perfectly grammatical:
He mustn't not never have done it to nobody.
and you can imagine that speakers might interpret this sentence by mathematically "unpicking" each negative just as you would unpick multiple negative signs when combined in a mathematical equation.
The problem is that this isn't actually how humans interpret negatives in natural language.
- (a) although it has a "logical" interpretation, humans will typically find a sentence such as the above, with multiple negative elements, very difficult to interpret.
- (b) there is a phenomenon where, at least in informal English, the interpretation of multiple negatives can depend on the intonation, which is sometimes difficult to represent in writing and can also depend on register.
Point (a) is, I think, illustrated by my sentence above. You can probably understand each individual negative, or even individual pairs of negatives, perfectly well. But taken together, you've probably no idea what the sentence actually means. I know I haven't.
As an example of point (b):
"I haven't DONE nothing!" will generally be interpreted as an emphatic version of "I haven't done anything!"
"I haven't done NOTHING!" will generally be interpreted as an emphatic version of "I haven't done literally nothing, but rather
something", "It isn't true that I have done absolutely nothing".
So pragmatically, for these reasons it's usually sensible to avoid multiple negatives in writing and rare to combine more than two in speech, bearing in mind that if you do combine them you may need to be careful with intonation, something that may not come easily to a non-native speaker. It's not that they're ungrammatical in principle. It's more that in practice they're difficult for speakers to deal with.
P.S. That said, I should have mentioned that multiple negatives are less problematic when each negative is in its own clause. So "I haven't done nothing" is maybe a bit harder to interpret than "It's not true that I haven't done anything". So if you must use a multiple negative, try and get each negative in its own clause.