I've had the plant for 4 yrs and now I have new shoots sprouting. I'd like to know if there is a way to remove them without damaging the trunk, to start new plants
Absolutely! Make sure they're at least 4" tall before removing them. Typically the best time to do this is in the spring, but if the pups (new shoots) are big enough and you keep them away from severe heat, you might be able to pull it off.
This article will tell you how: