Answer: What a fantastic plant!
Rather than division, I think your best bet would be to start some new plants from your old one by what's called "air layering". This technique basically injures a stem to induce it to form roots at the point of injury thus allowing you to eventually separate off a growing (and rooted) branch tip.
I'll try to describe the process here--but if you visit your library you may find a book with illustrations. It's much easier to do than to describe!
Begin by deciding where you want to cut the stem. I would try one of the lesser stems first, and observe what happens. About 18 inches down from the top, use a sharp knife to slice partway into the stem, about halfway is enough. Insert a clean toothpick or piece of plastic knife or some other little irritant into the gap to prop it slightly open. Now wrap the damaged area all around with moistened spagnum moss. Cover that with plastic wrap to keep it airtight and moist and affix it at both ends with tape. Check it periodically to be sure it is still moist. Roots should grow out of the cut surface into the moss. Once this happens, cut the branch off just below the roots, remove plastic wrap and plant.
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