It is demonstrated that higher-order plasmonic modes in the split-ring resonators (SRRs) are strongly enhanced when SRRs are arranged in a densely spaced two-dimensional array. The mode enhancement results from the near-field electrical coupling between the adjacent resonators. The effect is most pronounced in narrow gap SRRs which allows to observe experimentally plasmon modes up to the seventh order. In the array of narrow gap SRRs, the fifth-order resonance demonstrates high Q-factor, high resonance strength and wide tunability which opens up attractive features for practical applications of planar SRR structures.