First of all: I know that my request isn't compliant with the IMAP standard, but my mailbox is quite full and I want to store the mails externally on my private webspace instead of keeping them at my email provider.
So, the question is mostly in the subject! I would like to delete some(or lots of) mails from my email provider but I still want to keep them on my private webspace. So I'm asking for an option with a webbased email client which is capable of this. Another option would be to even delete the mails instantly after downloading them. POP is not an option, as it doesn't support folders.