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Format an IP packet with an invisible 2nd payload?

I think this is a question about IP packet headers—Can anyone think of a way to format an IP packet so that it would successfully be passed through all existing telecom equipment out there (that currently passes or routes IP packets), but contains a 2nd payload that specialized equipment could read? It's a matter of adding a non-trivial chunk of data (300-600 bytes) that wouldn't interfere with the normal routing of the packet or be mistaken as part of the standard IP payload as it traveled to its destination. The options field (when the Internet Header Length is > 5) might be exactly the type of thing I was hoping for, except IP packet format doesn't permit it to be anywhere nearly as long as it would need to be.

Presumably, it wouldn't work to include the extra data in the standard IP payload, because whenever the final recipient had normal rather than specialized equipment it would fail to correctly recognize the standard IP payload correctly. However, it can't (for example) be appended to the IP packet wantonly, because then the packet length would be wrong and it would all just be dropped (presumably by the first piece of standard equipment it encountered). So I conclude that it can only be done with a legally formatted IP packet.

Also, if the final recipient didn't have the specialized equipment, it would need to be handled as if it contained no 2nd payload. That is, the packet minus its specialized data would still need to be a valid "normal" packet.

Ideally, the extra data could be added to every packet, but if that is just impossible, then I wonder if it would be possible to meet the constraints above through adding an additional fragment packet.