We present a method of contraction that can be applied to re-construct the
recent extended non-relativistic and ultra-relativistic algebras as well as
corresponding action principles. The methodology involves the use of multiple
copies of Poincar\’e algebra. Consequently, the contraction defines
non-relativistic or ultra-relativistic limits of multimetric theories of
gravity. In particular, we show that the non-relativistic scaling limit of
bi-metric gravity corresponds to the recent formulation of an action principle
for Newtonian gravity with a constant background mass density.
