Mechanism with 38 joints (or other ways to solve it?)


I am making a pretty "complex" gripper/transfer-system. There are multiple linear manipulators, so that the entire grippersystem can move in x, y and z. On those beams 10 grippers are mounted which each have 3 ways to move. This results in a large amount of joints (38). When trying to create this in Robotstudio it says "can't compile", which I've understood is the limit of 12 joints that forbids me to do this. 

I therefore wonder if you have any idea of how I could make this work. One idea was to make the gripper a separate mechanism, and attach it to the transfer mechanism. Not sure how I would do that though, as I must attach the entire module. 

Below is a rough sketch of what I'm trying to achieve. 
The green and red boxes are identical grippers. But they need to move sideways on a common beam. I'm not sure how I could make them move sideways if I make them a separate mechanism.