Can I extend SER service cable to accommodate a new breaker box?
It is acceptable to splice additional wire to a feeder, as long as that feeder is not an unfused conductor (service entry). Keep in mind that improperly installed splice can become a real nightmare. It might be better to try and raise the new panel up if there are no obstructions rather than try extend the feeder. 

Also if an AHJ gets involved they may want to see if the panel has the proper clearances to legally install the splice. That would be wire bending area and proper fill.

Good luck.