One-way influence?

The standard way of looking at the interaction between English and another language is to say that English has influenced or even dominated the other language.  For example, here is what the leading Englishes advocate, Braj B. Kachru, says in Asian Englishes:  Beyond the Canon (2005), about English and Indian languages:  “There is general agreement that English has functioned as the main agent for releasing the South Asian languages from the rigorous constraints of the classical literary traditions.  With the influence of English literature came new experimentation, and resultant controversies.  The issues were seen in new theoretical and methodological frameworks.”

On the other hand, it is time to investigate what happens to English as a literary language when writers with a different mother tongue write in it.  I don't mean merely talking about how the language is different in literary texts written by second-language writers, because that has been studied quite well and even felt instinctively by readers.  I mean looking at English itself as a language.  There have been several studies of the number of non-English words that have entered English (I am talking of modern times, not the origins of English), but what about English structure?  Has the grammar of English changed because of the influence of Englishes or different varieties of English?  Has the English of monolingual American writers become different because of all the works written by immigrant or multilingual Americans?

I once gave a lecture on the influence of Philippine literature on American literature, and frankly, I was laughed out of the lecture hall.  Yet Herman Melville apparently passed by the Philippines on one of his whaling trips; given his sensitivity to languages and nature, he could not have possibly not been influenced by the Philippine writing then available to him.  Is it possible that the "strange" way he structured Moby Dick (usually attributed to his having dropped the project, read Shakespeare, and resumed the project without revising earlier work) been due to his experience reading the works of other countries (not necessarily the Philippines)?  Would it not shake the ego of Anglo-American writers to realize that they are as beholden to speakers of other languages as these others are beholden to them?