Can you cut a lucky bamboo in half and root both pieces??
The attached image illustrates my personal preferred method of cane propagation of dracaena. If you leave enough of the original cane on the 'mother plant', it is very likely that new branches will form, as well. It already has an established root system.
If course, this is all based on the premise that your dracaena is growing in soil and that you insert the cuttings into soil. I have no idea how this plant will respond if it's been growing in water for a long time.
Here is a link that might be useful:
Rhizo: Where is the top of that plant, LOL? Did you throw it away? Seriously though, can you stick the top portion (the part with leaves) in the dirt and have it root too? Mine has not been cut and waxed on top, it is growing in its natural form.
It's funny, everyone seems to grow these things for the stalks, but I prefer the leafy look myself.