The way to go about Co-branding would involve these major bits:
The background image/header would be a harmonius combination of all logos under one heading e.g. Commons
the logos in header would be linked to the organizations specific site
all videos would end with quick credits saying "this is a production by" - and the specific logo/name, followed by "in partnership" with the rest of the logos/names
Each organization would have the specific topic they are posting about setup as a playlist in the right sidebar, headed/branded with their name, and the most recent video would appear in the main box, where it automatically shows that it is related to one of the brands/playlists.
It would take long to implement the capabilities involved with possibility A, but B & C would only be more daunting (not because of the implementation of features) but the process of getting them from Youtube.
Co-Branding 4-5 ways
So there are multiple degrees of Branding on Youtube:
A) simple theme-ing that any user can do, though if used innovatievely can produce quite effective results:
Here is a page before themeing: http://awesomescreenshot.com/04e7jj051
and after some quick changes: http://awesomescreenshot.com/01e7jrs1d
If you have a Youtube account you can see the options for this by logging in and seeing toolbar at top of page:
Or you can see the options in these screen shots:
B) you can become a Youtube Partner to tap the monetary benefits of advertising: http://www.youtube.com/partners
C) you can get higher customization by getting a Brand Channel: http://www.youtube.com/t/advertising_brand_channels
The way to go about Co-branding would involve these major bits:
It would take long to implement the capabilities involved with possibility A, but B & C would only be more daunting (not because of the implementation of features) but the process of getting them from Youtube.
Some good if not obvious tips for a youtube channel -http://mashable.com/2010/04/26/branded-youtube-channel/