You can have trading accounts with as many brokers as you want with the same dp account. there are no particularly special formalities to be observed, just fill the trading account application form normally but do provide the information about the other trading account you have in the columns/space provided in the application form
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However, the investor must inform the DP regarding change in the bank account and corresponding change in MICR / IFSC code while updating their bank account details with DP. In the depository system monetary benefits on the security balances are paid as per the bank account details provided by the investor at the time of account opening. The investor must ensure that any subsequent changes in bank account details are informed to the DP.