  Mazur and Rubin have recently developed a theory of higher rank Kolyvagin and
Stark systems over principal artinian rings and discrete valuation rings. In
this article we describe a natural extension of (a slightly modified version
of) their theory to systems over more general coefficient rings. We also
construct unconditionally, and for general $p$-adic representations, a
canonical, and typically large, module of higher rank Euler systems and show
that for $p$-adic representations satisfying standard hypotheses the image
under a natural higher rank Kolyvagin-derivative type homomorphism of each such
system is a higher rank Kolyvagin system that originates from a Stark system.
