In short, no... you are probably best bankrupting after picking a better base. As a top tip, at this stage of the game I would look at airports with Pax ratings between 35-55%, and aim to develop an airline using medium aircraft, ideally turboprops 50 pax up.
The rules for other bases are that you need to have had an airline for 18 months gam-time, and have 15+ aircraft in operation. Only then can you open a new base and fly routes that do not involve your HQ airport.
In future versiosn I believe we may get options to do an HQ --> B --> C --> HQ type flight, but not yet - and it wouldn't help you much in any case.