I am not aware of any Clipboard information managers that currently might be able to do what you require, though NoteFrog had rather looked as though it might be heading in that direction, eventually.
I use CHS all the time, and I find it to be an amazingly useful tool. I would be very interested in the possibility that it might be made to do what you are requiring, as I have long had the same/similar requirement.
However, the way I currently meet my needs in this regard is by using MS OneNote (part of MS Office) as the intermediate storage medium of material that I wish to keep the formatting of. It has become my primary PIM (Personal Information Manager).
You could also consider Zotero and Wezinc (both $Free) for these purposes. Wezinc integrates with (hooks onto) the Clipboard such that if you copy anything to the Clipboard, Wezinc asks you if you want to also save it into the Wezinc database. I'm still trialing Zotero and Wezinc - mainly as alternatives to the excellent Firefox extension ScrapBook, so am unable to give a conclusive view as to whether either could be useful for your purposes.