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One of my cousins grew up in a Thai speaking family, had Burmese people as nannies and been studying in an international school. She speaks perfect 3 languages... No harm learing 3 languages here. She's a normal little girl :)

No doubt she is normal, she must be very smart, too! What happens with children like that, according to linguists, is in their early years their vocabulary range in each particular language is smaller than monolingual children's in that particular language. However, if you count the words of the bilinguals (or trilinguals ;)) in all languages they speak it equals the monolinguals' vocab range! It can, of course, be compensated for when they are a bit older.

I used the one parent one language method from birth for my daughter who is 7 years old now. She gets Thai from Mom and French from me. She gets English from school, cartoons and games. She is more advanced in English and it looks like her mother tongue is English, perfect prononciation. She is catching up with Thai now, at first she sounded like a Farang speaking Thai! French is weaker because I can't compete with the amount of hours she is exposed in the 2 other languages. A 2 hours per week lesson at the Allience Francaise is correcting this. The vocabulary she has is different for all 3 languages.

This is fascinating and it must be very rewarding to be a parent of a polyglot child!