An education professor at Pace University wrote a book on her experience raising her hapa sons to be trilingual (Chinese, English, + another category 1 language, up to 11 years old in this book). I don’t own the book and don’t know her sons’ proficiencies in the three languages.
One of her take on trilingual proficiencies is that one can’t judge the proficiency of the various languages using the same measures as monolinguals. I, of course, agree on that part.
Here are two parents’s take on learning three languages from another site:
Parent A: 我老公講英文 我對小孩中文 但小孩回我英文…..兩位小孩三歲就出去上整天的 英文/西班牙文雙語學校⋯ 他們現在 已經 three languages la…. 還很小⋯ 五歲跟三歲半⋯
My take on it: 每個家庭的期許不一樣。我希望小孩子在國中時就可以流暢的看中文小說（才不會排斥能以中文書當娛樂）。我想這一定要從小中文基礎很強，口語非常強應該是避免不了，但這樣就沒太多能花在其他語言的上面，因為還要花時間補英文或其他科目或才藝。這ㄧ方面，我們是先精再廣。 Every family has different expectation, means, or goals. For us, I want them to be able to read Chinese novels fluently in middle school. I think this require very strong Chinese since they are little, including colloquial Chinese. This really limits the amount of time one can invest in a third language (at least till the goal is almost reached), since they will have to spend a good part of that time working on their English, other subjects, or extracurricular pursuit. So, in this regard, our method is “Depth first, breadth second”.