We show strong coupling involving three different types of resonances in plasmonic nanoarrays: surface lattice resonances (SLRs), localized surface plasmon resonances on single nanoparticles, and excitations of organic dye molecules. The measured transmission spectra show splittings that depend on the molecule concentration. The results are analyzed using finite-difference time-domain simulations, a coupled-dipole approximation, coupled-modes models, and Fano theory. The delocalized nature of the collective SLR modes suggests that in the strong coupling regime molecules near distant nanoparticles are coherently coupled.