  We consider a Lagrangian system $L(q,\dot q) =
  \sum_{l=1}^{N}L^{\{l\}}(q,\dot q)$, where the $q$-variable is treated by a
Generalized Additive Runge--Kutta (GARK) method. Applying the technique of
discrete variations, we show how to construct symplectic schemes. Assuming the
diagonal methods for the GARK given, we present some techinques for
constructing the transition matrices. We address the problem of the order of
the methods and discuss some semi-separable and separable problems, showing
some interesting constructions of methods with non-square coefficient matrices.
