Probably.
Your question is analogous to:
"I have a car with a battery in it. Can I put a bigger one in it?"
10Wh is an absolutely TINY battery. 20Wh is half as TINY, but TINY too. Do you mean Ah?
Are these lead-acid batteries?
Assuming the system can use the full 120W of the panel for battery charging (equipment can capture it all, panel is favorably mounted, no shading), 120W / 14.4V = 8.3A
Most lead-acid batteries like to be charged at 0.1C or 10% of capacity, so I would expect you could go as large as 80Ah.
If you have a manual on the system, that would help.