  We generalize the idea of relaxation time stepping methods in order to
preserve multiple nonlinear conserved quantities of a dynamical system by
projecting along directions defined by multiple time stepping algorithms.
Similar to the directional projection method of Calvo et. al., we use embedded
Runge-Kutta methods to facilitate this in a computationally efficient manner.
Proof of the accuracy of the modified RK methods and the existence of valid
relaxation parameters are given, under some restrictions. Among other examples,
we apply this technique to Implicit-Explicit Runge-Kutta time integration for
the Korteweg-de Vries equation and investigate the feasibility and effect of
conserving multiple invariants for multi-soliton solutions.
