You can only open one trading and demat account with the same PAN.
However you can open a new trading & demat account in the name of your company, LLP, partnership firm or HUF even if you have an existing account since the PAN will be different.
Where can I create a fixed deposit account?
How do I open an account online?
What documents are required to open an account online?
How long does it take to open a Demat and Trading Account online? How do I track it?