I would say that it is more two two-man story RPs that are linked by their participants rather than one single four-chapter story.
Essentially, we treat it like BarboSaboteur and Action SHIT are the tag teams rather than SaboSax and BarboSHIT, except we highlight the connection between the four RPs with why they are actually working together ie. Depressive's want to expose SHIT to different types of personality - the idiot focus groupers and the flamboyant Saxton, while keeping Manic and Smoker entertained by having fun/trying to kill Saboteur and SHIT's continued want to discover more about being human.
What SaboSax's motives for the crossover are beyond the earlier suggestions of a quest for SHITs "upgrade chip" (perhaps Barbosa and Saboteur get as far as reaching the lab where SHIT was created?) and Saxton wanting input for his movies, which ends in a SHIT (pink box) makeover.
To be honest, the trickiness comes in when it comes to the focus of the RPs as the story of mine will link to that of Saboteur but the character development needs to come more with SHIT in mind. Miko would have a similar burden - dealing with Saxton but focusing on Barbosa and the Bearded Gents.
Perhaps we could all have an internal monologue section of our RPs to explain not just the motives of our characters but also to help link them together, with Saboteur wondering what Saxton is doing, Barbosa arguing with himself over their plan for SHIT, Saxton wondering what he did to get lumbered with such a un-hip robot cat while SHIT, as the only true straight man in this world of madness, is just wondering what the hell is going on full stop.
Such monologues should also help focus the RPs on their opponents.