  We study the uniform boundedness of solutions to reaction-diffusion systems
possessing a Lyapunov-like function and satisfying an {\it intermediate sum
condition}. This significantly generalizes the mass dissipation condition in
the literature and thus allows the nonlinearities to have arbitrary polynomial
growth. We show that two dimensional reaction-diffusion systems, with quadratic
intermediate sum conditions, have global solutions which are bounded uniformly
in time. In higher dimension, bounded solutions are obtained under the
condition that the diffusion coefficients are {\it quasi-uniform}, i.e. they
are close to each other. Applications include boundedness of solutions to
chemical reaction networks with diffusion.
