general relativity - Is Einstein-Hilbert action the unique action whose variation gives Einstein's field equations?

I know that

1. 
   

   scaling the action with a non-zero multiplicative constant, or

   
   


2. 
   

   adding a total divergence term to the Lagrangian density

   
   
   

do not change the Euler-Lagrange equations, cf. e.g. this Phys.SE post.

Apart from such trivial modifications (1&2), is Einstein-Hilbert action the unique action whose variation gives Einstein's field equations? If not, is there any other action known which differs non-trivially from Einstein-Hilbert action and whose variation gives Einstein's equations?