Compositionality and English

It is widely assumed that natural language must be compositional in the sense that the meanings of sentences must be determined by the meanings of words and their order of arrangement in a relatively straightforward way. Typically, this is thought to explain the productivity of language: we are able to produce and understand novel sentences because we have a recipe for interpreting their meaning. However, there are other ways to understand productivity, because the meanings of sentences might be determined by things other than the meanings of words and their order or arrangement.

Imagine a variant on English that was identical to English except that in this variant, alliteration introduces sentence-level negation. Thus "dead dogs tell no lies" in this variant means what "its not the case that dead dogs tell no lies" means in ours and "five fat frogs ate five filthy flies" means what "its not not not not the case that five fat frogs ate five filthy flies" does in ours.

I take it that the meanings of individual words in this variant are the same as the meanings of the same words in English. In the vast majority of contexts, words are used in exactly the same way. However, the meaning of sentences is stipulated to be different. The meaning of sentences are determined by factors other than the meanings of words. They are in part determined by the spelling of words.

This language is productive and one that we could easily all learn to speak. Maybe we couldn't ever become fluent in it. That seems to me to be an empirical question. However, there could be creatures who could speak it as effortlessly as we speak English.

There isn't anything in English as clearly non-compositional as this variant. However, it is far less obvious that there are no non-meaning properties of words that go into the determination of meanings of sentences.

Here is another English variant that is non-compositional, but in a slightly more plausible way. In this variant, speakers substitute interpret noun phrases in terms of prototypical instances. "I have a pet" might mean what "I have a dog or cat" does in  English, because dogs and cats are prototypical pets. "I have a pet fish" might mean "I have a goldfish", since goldfish are prototypical fish. The meanings are determined by prototypicality associations as calculated by human minds, but the meanings of individual terms don't build in all of their prototypical instances. One cannot derive the fact that goldfish are prototypical pet fish from the fact that dogs and cats are prototypical pets. The fact that goldfish are prototypical fish is not part of the meanings of 'pet' and 'fish'.

Might English be non-compositional in something like this manner? It seems to me to be highly plausible that it is. But it is an open empirical question.