Yes, you can have as many demat/trading accounts that you want, but you can’t have them with the same broker/DP. So if you have one trading account with Zerodha or 1 demat with ILFS, you cannot open another one with Zerodha/ILFS, but you can go out and open with others.
The disadvantage which such a thing is that you will have to keep track of two accounts, login to two separate trading platforms, separate P&L statements while filing your taxes and all.
You can link the same bank account to multiple trading accounts.
When you buy shares, you can send the shares to the same demat through multiple trading accounts. But while selling, you will be able to do so only through 1 trading account, the account for which you have the POA mapped with the demat. POA is required to debit shares online when the shares are sold.