This made me think of how many languages are spoken within my family - including partners and kids - I think it comes to about 10, with varying degrees of fluency!
My daughter has always been fascinated as to why people speak different languages. Her own exposure, in order of fluency, is English, Thai, Laos, Italian and Japanese. She is 10 and English is now definitely the dominant language.
However, I do have a friend in a similar situation to you in that he is French, wife is Thai but they really wanted their kid to speak fluent English, hence the switch to an English International School. Their son is now pretty fluent in all 3 languages.
My own experience as a bilingual child - although also exposed to other languages - was that the languages "stuck" around the age of 8; before that, it was easy to lose fluency by changing country.
Like you, I was adamant my daughter would speak to me only in English; the funny part is that she also prefers speaking English to her mother!
Good job in having a thought-out method to ensure your daughter has the best possible language skills.
Thank you very much @rycharde for explaining your experience with raising a multilingual kid. When it's done early it's easier to assimilate languages.