You don't need to create any additional tables or fields. In fact, you shouldn't because this is just redundant information.
All you need to do is look for any items that started before (or during) the week (or day) in question and ended after (or during) the week (or day) in question.
Not only does this simplify your task of finding appropriate matches, it keeps your database clean. You should never be adding extra junk to your database for the sole purpose of making your coding easier. It will make your coding easier ONE TIME and then it will make maintenance of your application a nightmare for years onward.