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G. E. Hutchinson raised the paradox of how a number of phytoplankton species competing for the same resources are able to coexist in a relatively isotropic environment. As a key for solving the paradox, we focused on the limiting similarity which prohibits the coexistence of similar species. We expected that the limiting similarity will be mitigated by some factors which are not represented in traditional theoretical studies but can be represented if we use a three-dimensional (3D) model. The use of a 3D model enables us to explore the limiting similarity without using the controversial assumption connecting niche overlap with the competitive exclusion in previous theoretical studies. Furthermore, while constant or no dispersion is given in theoretical studies, it is explicitly represented in a 3D model. The coexistence of similar species in 3D environments was explored by dividing a target persistent species in a quasi-equilibrium community into 80 subspecies, which were slightly different from one another at the optimum temperature for population growth. In the experiments, we found cases in which several dozens of species having nearly-overlapping niches coexist stably at a point for over 80 years. The comparison of experiments with and without dispersion by oceanic currents revealed that dispersion negates the progress of competitive exclusion or significantly delays the exclusion. The result that species having nearly-overlapping niches are able to coexist also highlights the crucial role of the specific rate in determining the number of coexisting species. If the number of coexisting species is not determined by the limiting similarity, it will be determined by the frequency of speciation events, as in the neutral theory.