Ok, I think I understand how to make this work. Bear with me, this is going to be a LONG post (And a lengthy implement)
The job begins at multiplayer lobby. When you start a new room, in ANY play mode (As this could work with any version of Osu!, bear with me) you have the selection of "Solo" And "Co-op"
When you enter a co-op mode, the Difference will be at the beginning - you are given a list of the songs that are CO-OP applicable (Sometime after this implement these maps will start beginning.)
By picking the map, it sets up the room to play it, with a max amount of players for the song (one for each part mapped) And players can join the lobby. The host can choose to assign parts, to Roulette parts, or to let the players choose from a sort of pool. Sort of like a character select. The host can also, choose how the fail mode is set up - fail by part (one person drops) - Fail by majority (1/2+) - No fail.
When you enter the game, You'll see a statistic on the left, not for score, but rather a latency readout and, as the game updates, it identifies player health.
The map layout will be as any normal MP map, except since the map was already made for Co-op, the function would make the notes of all parts appear, but only as a (Faint) shadow, in time with your own. You wouldn't see the hit animate or the cursor, too much background interference, but it'd give the player a sense of the other part / parts. There would also be no score part, too much lag sending that type of information.
At the end, the totals of each player are added up, and the video file is saved as LOCAL as your own solo replay, any teams that would match the top 40 (adjustable) would be combined as a whole and posted as GLOBAL, this would show each part acting in harmony.
To incentivise the creation of such maps, The difficulty min + Max would be altered severely if it is made for co-op - maybe just to have the Difficulties work separate (As they would still work as normal maps [A LONG LONG LONG IMPLEMENT] and could be counted as individual diffs) And priorities should be given towards these maps until there is a sufficient stock of songs and Genres.
Summing it all up:
New possible codes used to create maps - having them act as one when needed
Alterations to the Multiplayer lobby
Change in Multiplayer display to be added as a CO-OP mode
Secondary tables for CO-OP scores on a song
Boosting mappers willing to make such maps
Hell to Osu! supporters, Maintenance, and Programmers alike.
I'll star this idea in the fact that I'll see it come around in my child's generation XD