@moogiemar – not a direct way and not copy/paste, but you could use Export to IDMS to create snippet files, that you can place. That is working in both directions. InDesign CC <=> InDesign 2014 (with the usual caveat of feature compatibility between the two versions).
Draging selected objects on the page to the file system will also create IDMS files. You can drag them from the file system into InDesign or use the Place command. The place gun will be populated and with the alt modifier key (Mac OSX) you could place the object(s) in place.
Or use Adobe Bridge to manage and place the IDMS files.
What's also possible:
Create and use a InDesign library file to store the objects and place the assets from that library.
When working with library files it would be best to create one from InDesign CC and one from InDesign 2014 for adding and removing assets. You can open the same library file in both InDesign versions. Library files are agnostic to InDesign versions.
Uwe