I don't know if it's what you are looking for but I wrote a plugin for duplicating objects in Carrara. I've never used Bryce so I don't know how differen it is. The plugin can be found here...

http://www3.telus.net/robbert/zekaric/devWork/carraraPlugindoc/zdup.html

Otherwise it's a matter of copy, paste, drag, and paste again to get similar offsets as the previous paste. Carrara doesn't have a duplicate other than that.