There's empirical work on this [1] (alas, paywalled): multiple center embedding in speech is rare but exists. It is more common in writing. There are examples

There's empirical work on this [1] (alas, paywalled): multiple center embedding in speech is rare but exists. It is more common in writing. There are examples of 2 levels of center-embedding which are clearly grammatical and not hard to understand: > Anyone [who saw the woman [who committed the crime] at any point] should be questioned. Others are very hard to understand: > Anyone [who the man [who the woman shot] killed] should be questioned. There are many factors that make a sentence hard to understand, not just degree of embedding. Some degree 2 sentences can be easy, and some degree 1 sentences can be hard (e.g. "the horse [raced past the barn] fell", which has only 1 level of embedding). So if you want to describe English with the rule "no embedding beyond 1 level" then you're going to miss a lot of valid sentences while also failing to rule out lots of invalid ones. Contrast this with a valid descriptive rule of English, such as "determiners such as 'the' always come before the nouns they modify". I can say "the man died", but "man the died" is never comprehensible under any circumstances and cannot be made better. No one would say that a sentence with 10 levels of embedding is perfectly fine English. But descriptively, you have the problem that there is no non-arbitrary upper bound on embedding degree: it's not clear when one more level of embedding takes you from grammatical to ungrammatical, and furthermore it depends on the contents of the embedded clauses. There is also some work I'm aware of, currently in prep for publication, showing that the extent to which people can understand multiply-embedded sentences strongly correlates with IQ (measured by Raven's matrices). All this suggests that the simplest descriptive rule is to say that English allows center-embedding recursively, but that there are human processing limitations on sentences that create very deep stacks. The "human processing limitations" part is basically the whole field of psycholinguistics: many details have been worked out, but many details are still sketchy. [1] Karlsson (2007): http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=1056752 http://journals.cambridge.org/action/displayAbstract?fromPag...