Yes, it is possible. You can take loan from any number of banks but this is generally not advisable as this will add to your monthly EMI burden. Your chances of securing a loan decrease if banks think you have too many existing debt obligations for your income level. There is a good chance that you will be rejected for a loan as lenders are nervous that you will not have the capacity to fulfill your obligations.
Instead of 2 loans, it is better to apply for a much higher loan amount from one single lender – if you qualify.