Can wife of HSP (ii) start a business?

I am wondering if a wife who is staying as a dependent of a highly skilled professional (ii) can start her own business without changing the status? Anyone in this group has such experience in Japan? Please share. Thank you.

For the question as phrased, my understanding of the rules is "no".
Even if you got the permit to engage in activities (work) as a dependent, that would limit you to 28 hours per week, and normally assumes you are working for someone else (i.e. someone is paying you).
If you want to set up a company (which anyone can do) and then work on that business, then you need the correct status of residence for that activity, and "dependent" is not the correct status.