Yes you can open multiple Trading Accounts (not with a single broker) and multiple demat accounts (not with a single DP), no restrictions on that. Also, one demat a/c can be mapped to multiple trading accounts, no issues.
Advantages of two or more Trading a/c’s: NOT MUCH, may be little bit of reduced brokerage and/or different trading platforms (depends on your individual taste/likeness)
Advantages of two or more Demat a/c’s: NOTHING
Disadvantages of two or more Trading a/c’s: You have to bear account opening charges, you have to keep track of activities in two or more trading a/c’s.
Disadvantages of two or more Demat a/c’s: You have to bear annual maintenance charges of Demat a/c’s whether you use it or not, you have to bear the charges (approx. Rs. 500/- or so yearly, depending on the DP)
As per me, it does not really make sense to open multiple trading a/c’s and demat a/c’s.