GST registration and ITC

Dear exeperts,

one of my client is already registered under GST as chemist as proprietor.

My query is can he open another proprietory firm under same registration within same state, with same trade name or different trade name also with same place of business or different place of business? product is different and the business is different (trading) not chemist.

if different business under same registration is allowed, can itc of these different businesses/products allowed ?