You can, but not now, should be done in spring, see link below

http://homeguides.sfgate.com/multiply-nandina-34620.html

Wow Bamboo - that's brilliant. I have 4 varieties, and had no idea they could be divided - thank you!

I didn't know either, Sheilabub - I just googled it, and that link came up. Doesn't say you can divide them in my RHS encyclopaedia... All the American sites say you can divide them, but none of the UK ones do - I;ve just checked the RHS and they say propagation is by seed or semi hardwood cuttings, doesn't mention division. I don't think I'd risk it unless it was a very large plant with a big rootball...

Thanks again - I'll stick to taking cuttings . .