Request to increase credit limit or open a new credit card?

[bawsanova]

Hello,

I am new to credit. In 2012 father opened an auto loan in my name to help me establish credit. In 2014 the loan was paid off and closed.

This is the first credit noted for me. In 2018 (late November) I opened my first credit card. I was approved for a $1400 credit limit.

It's now almost been 4 months and I'm most likely at 6 months going to either request a credit limit increase or open a new credit card. 

I was wondering which I should do first or if I should do both? Wanting to know what options would be best for increasing my credit score / prepare for increasing in future. My current credit score is ~770. 

Thanks,