aggregating posts

Hello.
I have a website that covers our community pool’s swim team. I’d like to create another site that aggregates content from the websites of other swim teams in our league.

Here’s the flow I have in mind:
1. Each participating website contacts me to express interest.
2. The participating website tags or some how marks the posts that they want to share(e.g. leagueX).
3. The website that combines all of the posts (i.e. aggregator site) would then look at each participating site to see what posts are new.
4. The beginning of each new post would be added to the front page of the aggregator site with a link to read more. The ‘read more’ link would go to the full article on the aggregator site (not on the contributing site). The full article would include credit information like which swim team provided the post, the date, and a link to go the original post on the contributing website.

Is there any plugins, themes, etc. that already do this? All suggestions are appreciated. Thank you!