Looks like you are asking your MTA to do what is usually done by a MUA. Most email readers capable of multiple accounts will be able to collate the mail. If you are looking for a way to collate it before you actually get to read it, then you should be able to configure your collection agent (like fetchmail) or your MTA (exim has quite a bit of usefulness, as does qmail) to dump all inbox material into the same folder (may have to change a config to do so). But, I would suggest that you use a MUA like Opera M2. That way, all your mail is collated for reading when you view it. Its is also searchable through various "views", so that you can filter it by contact, subject, content, attachments, addresses, state, etc.
For remote retrieval of this mail, I think that you may have to set up a mail server that uses your maildir for its "source". Due to the scope of what you need to accomplish, it looks like you have two choices. You can collect the various packages required to do the tasks you require and read a lot of man pages and config files (which will make you the email guru) or you can just use a multi-account capable MUA like Opera M2, Mozilla mail, Thunderbird, Kmail, Evolution, or Mutt for that matter and configure the program to "leave messages on the server" for the POP accounts. That way, if you do it locally, or remotely, you actually are just skipping a step and leaving all your email with their various servers, deleting the ones you want, when you want, from where you want. Depends on how much you wanna read. I have opted for #2, as I am not sure how long my ISP would let me serve my own mail.