You don't have to be within my institution to collaborate with me; I can help you succeed (e.g. publishing top papers or landing top jobs) without ever being my official/internal student, as I have done many times in the past.
Try my open mentoring program, as it can benefit you one way or another.
The amount of efforts I spend on a project is proportional to your productivity, rather than your official affiliation. Other things being equal, I prefer external collaboration due to greater flexibility.
I am taking interns with Adobe Research but not students with HKU right now.