Can a person have more than one trading account with a broker?

No. As per the Regulatory guidelines you cannot have more than one trading account in the same name with the same broker. Hence, you cannot have more than one trading account in the same name with a perticular broker.

But you can have as many trading account as you want with different brokers using the same name. For example; you could have an account with ICICI Direct, Sharekhan and ProStocks. All at the same time with same name.