Yes, you can convert a regular demat account to BSDA, but it depends on the depository’s monthly verification of your holdings and investor status. 

Before requesting to convert, ensure you don’t have other demat accounts in your name, as having more than one will lead to rejection. If your holdings exceed ₹2 lakh or you open another account after conversion, your BSDA will be treated as a regular demat account and you will be charged AMC as per regular demat account. Tap here and look under Tariff for Demat Account for details on AMC