Why is N=4 SYM's Lagrangian Unique?

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Hello, I've seen stated in many places that N=4 SYM is a unique theory and I'm wondering why this is. In my reading, I've seen why there is a unique N=4 supermultiplet and this would fix the field content of the theory (up to one caveat I have: why couldn't an N=4 theory contain multiple N=4 supermultiplets interacting among themselves?). However, I haven't been able to find anywhere why the Lagrangian should be unique.

Thanks!
 
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