Yes you can add the first pack to the second to increase the run time.
The current packs are 2S2P
two cells in series (2*3.6volts = 7.2volts) and
two cells in paralell (2*2200mAh = 4400mAh)
The new pack should be 2S4P
two cells in series (2*3.6volts = 7.2volts) and
four cells in paralell (4*2200mAh = 8800mAh)
You would also have the option of making two packs one biggish using 6 cells (2S6P) and one mini using 2 (2S1P)
This link may help. It also shows how to connect balancing leads to be used with a balancing charger. It should be noted that the circuit boards are protection circuits preventing overcharging and over discharging of individual cells but does NOT make sure that all cells have the same voltage ie are balanced.