  We present an alternative approach to the vector version of Krasnosel'skii
compression-expansion fixed point theorem due to Precup, which is based on the
fixed point index. It allows us to obtain new general versions of this fixed
point theorem and also multiplicity results. We emphasize that all of them are
coexistence fixed point theorems for operator systems, that means that every
component of the fixed points obtained is non-trivial. Finally, these
coexistence fixed point theorems are applied to obtain results concerning the
existence of positive solutions for systems of Hammerstein integral equations
and radially symmetric solutions of $(p_1,p_2)$-Laplacian systems.
