The 'clipboard manager' would need be aware of which program was currently active and either hide or gray out clippings which could not be pasted into the selected document/field/project/track.
It's not up to the OS, or the clipboard manager to know what data types can be pasted into any given destination - the application does that.
In actual fact, the current clipboard implementation already supports storing multiple data sets - for example, if you copy text from a word processor, the chances are it's copied in multiple formats - there may be a rich-text version that includes font and style data, as well as a plain-text version with just the raw text. It's up to the receiving application as to which data is retrieved when you paste.
(yes, I realize this is a slightly different issue from multiple clipboards, but it does pertain to storing multiple objects on the clipboard).
I use a few built in multi-key shortcuts on a regular basis, the first one that comes to mind being ⌘⇧Z (redo).
Ahh, but that's not the same thing - or at least not what we're talking about here. That's just a modifier (shift) applied to the ⌘Z.
In this case what State and I are referring to is one technique implemented by at least one third-party app. Let's say your clipboard manager supports 10 clipboards - called Clipboard 0 through 9. To copy something to a specific clipboard You press the ⌘ key and C (to copy), and while still holding the ⌘ key you press the number of the clipboard you want to copy to - so to copy to clipboard 5 you ⌘-C-5.
Similarly to retrieve something from a specific clipboard, you press ⌘ plus V, then the number of the clipboard you want.
The problem with this approach (and I've used such a beast in the past) is that it really gets in the way of your workflow, because the copy (or paste) isn't effected until you let go of the command key. So now you can't use ⌘-C followed by ⌘-Tab to switch applications - you have to ⌘-C, let go of both keys and then ⌘-Tab. Sounds minor, I know, but try it sometimes - you'll be astounded how often you hold that command key between multiple commands. Implementing a system-wide 'feature' that requires you to release the command key to effect the command is a real distraction.
Just watch yourself use command keys in daily life - see how you learn and expect an immediate response when you press the relevant letter/number key. Imagine what it's like if that action waited until you let go of the command key.
Ultimately I think multiple clipboards is something that a subset of users could benefit from on a regular basis (I use one myself), but is a user-specific/custom requirement and therefore a task best served by third-party apps.
