Excluding text, objects from Feed

Although I already found an alternate topic or similar issue (excluding categories from feed), I was wondering if anyone knew how to prevent certain parts to be excluded from the feed?

When I use the “more” button, I was hoping that the text that followed and the objects wouldn’t be included in the feed.

I’ve tried deleting the enclosure, but that doesn’t work. (It is automatically included again).

So I guess if there is no way to do that, then could a new feature be developed to include a link in the feed to view the attachments and other stuff at the post page?

I still want to send complete posts through the feed, but handpick (by using the ‘more’ tag twice or something) certain posts with which the remaining text/objects won’t be loaded.