Noam Chomsky has argued that humans have a deep grammar from which our languages emerge. Steven Pinker’s work tends to confirm this insight.
In Moral Minds, Marc Hauser has argued that there is likely a deep grammar of morality. I would tend to agree. There is a deep sense of “unfairness” in a lot of species, including humans. Humans also have a set of moral universals–prohibitions on murder, incest, theft, etc.–with cultural variations and individual subjective interpretations within those cultural expressions of those universals.
Music is also considered to have a grammar out of which the various musical expressions emerge.
Stories also have a grammar, and one could argue that each sentence is in fact a miniature story. Meaning, stories follow the grammar of language at scales of greater complexity.
Let’s go deeper. As it turns out, proteins also have a grammar. And if peptides do, certainly genes and the DNA itself do.
Do cultures have a grammar? Economies? Technological innovation? It would be odd if they didn’t.