My son was exposed to 4-5 languages at home since young too - and I can tell you that he now understands them all very well! BUT, you have to make the effort to try and let one person use only one language with him - or at least NOT to mix them together during a certain activity. Meaning, the same person can talk to him in two languages - BUT only one at a time (eg. Reading activity in chinese, then when reading is over then use english for play time etc).
I'm saying this because my son had isolated speech delay - and the two main reasons we could identify was 1) my parents liked speaking multiple languages to him at the same time = he got confused about which word he should use in what language to ask for what he wants and 2) my parents (main caregiver while I was finishing my studies) were always giving him the things he wanted without him even asking/pointing to them = he never really had the need to express himself.
He took about 10 months of speech therapy and also been in childcare for 6 months now, I also took over looking after him as soon as I graduated, so he's currently having a 6-month interim break from speech therapy before another assessment - but it was a tough and long 2.5 years before he could catch up to his peers in terms of speaking.
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Mommy of 1 cute boy