Not sure how to achive this is DxD2004, however I question whether this is a good idea or not.
If you copy 4 parts from page 1 of the schematic to page 2 of the schematic with the RefDes staying the same, then I believe you will then have problems when you come to package the design, as you will have at least 4 parts with the same RefDes.
Surely if you just copy the parts (without RefDes) then when you package the schematic new RefDes will be added to the components.
It is more for that we use an existing starter block so instead of doing a full copy of the schematic page and renaming it as my schematic id rather just copy the starter symbols and their refdes and not have to go completely through and rename everything. someone has already done the work of naming the refdes's and it would be quicker if i could just copy and paste with the refdes's attached.
You can always work from an archive copy and delete what you don't need...