The idea is great, but in my opinion it'd be a nightmare.
I 50/50 split previously with a good friend and it worked perfectly, but there was no need for a written agreement - everything was split 50/50 - still pee'd us both off though when one of us decided it needed new tyres or a refresh of suspension, bushes, new clutch, service etc. Or one of us had a better day than the other due to the other one killing the tyres on the previous session due to driving like a t**t trying to chase down someone ...getting red mist haha. But we still split 50/50 - as that was what we agreed.
In the end he bought me out as family life took over for me and I couldnt get to the track as often as I wanted to.
I also agree with
@GrahamS above - we had different ideas on mods too, plus tyre specs, car set up - who was trailoring it this week, which meetings to attend, which weekend we were racing etc. We always came to an agreement, but we compromised with each other and wre best mates.
Will your MD be as flexible ?
That was with a mate who I had (and still do have) a lot of time for - no written agreement needed and a written agreement would have only made any frustrations worse I believe. There should be enough trust and respect whereby its simple, split / dont split - no argument.