Adding headers to email forwards?

I have a domain with email hosted with DH. I have a number of forward-only addresses for an individual. For example, for Tom Jones I have a real address tomjones@ourdomain, and forwards to that address for tjones, tj, tom, etc. If email is sent to tjones, it goes transparently to tomjones. That all works great.

For some purposes, the tomjones@ account might itself forward to tttt@jones.tld, as maybe this is where Tom prefers to get all of his email for various domains.

In the headers for email received at jones.tld, we see the To as tjones, which would be where the originator addressed the mail, but there is no reference to the tomjones@ address. Remember that tjones forwards to tomjones, and tomjones then forwards to tttt. It would help to be able to see that intermediary address somewhere in the headers.

Why? When Tom gets his email at tttt he wants to filter it. Some mail will go to him personally via tomjones@, tj@, etc., but other mail might go through sales@, support@, or some other address, and Tom doesn’t want these in his personal inbox. If we have that middle-point identified in the headers, we can sort/filter email addressed directly to him, as it will all be coming through tomjones@ourdomain. The alternative is that client-side filters need to be created for every alias which may be present in headers, and a final @ourdomain bucket will allow Tom to catch anything not specifically for him, but still somehow ending up in his inbox.

So the ultimate question is, can we add headers into email forwarded in DH? Can we add headers at the server to anything inbound or outbound through the DH mail server - maybe through the new API? We use software for sending mail out through the DH servers, and of course we add headers there, but now I’m hoping to get better control over the inbound mail.