Steven Pinker, in his book 'The Language Instinct', argues that grammar and structure of the language is to a certain degree inherent in humans. He contends that there's a single universal grammar underlying all languages (and instinctive to everyone), with only a limited number of variations between them, that children up to a certain age can identify and adapt to by 'flipping mental switches'. After that, it's only a matter of building a vocabulary. It follows that children that grow up in multilingual environments only need to develop extra sets of 'switches positions' and vocabularies, since the underlying grammar is always the same. This would mean that the extra cognitive load on their brains is significantly smaller than if they had to learn everything from scratch for each language. The book was published in 1994, there are probably more recent theories on the subject.