  Symplectic partitioned Runge--Kutta methods can be obtained from a
variational formulation where all the terms in the discrete Lagrangian are
treated with the same quadrature formula. We construct a family of symplectic
methods allowing the use of different quadrature formulas (primary and
secondary) for different terms of the Lagrangian. In particular, we study a
family of methods using Lobatto quadrature (with corresponding Lobatto IIIA-B
symplectic pair) as a primary method and Gauss--Legendre quadrature as a
secondary method. The methods have the same favourable implicitness as the
underlying Lobatto IIIA-B pair, and, in addition, they are \emph{P-stable},
therefore suitable for application to highly oscillatory problems.
