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By means of standard Thomas–Fermi approximation, we present stable solutions of one- and two-dimensional (1D and 2D) multihump soliton structures, including 1D and 2D modulated solitons as well as 2D soliton clusters, supported by inhomogeneous defocusing nonlinear Kerr media. Such nonlinear settings may apply to nonlinear optics and Bose–Einstein condensates. All the 1D and 2D fundamental modes with different numbers of humps (for both modulated solitons and soliton clusters) are demonstrated to be robustly stable. Besides, the considered 2D nonlinear setting also supports a vast varieties of vortex modes—vortex soliton clusters. Such novel type of vortex soliton clusters is qualitatively different from the ordinary vortex clusters, on the account of the fact that the latter type is a single large soliton with several-vortex configurations inside it, while our predicted vortex clusters structures are composed of the arrays of unitary vortex solitons. Stability regions for all the soliton structures are identified via linear stability analysis and direct simulations. • Approximate analytical solutions of modulated solitons and soliton clusters under inhomogeneous defocusing nonlinear Kerr media are obtained. • The solutions are produced by means of the standard Thomas–Fermi approximation. • Modulated solitons, soliton and vortex clusters are demonstrated to be stable profiles under such inhomogeneous defocusing nonlinear media. • The modulated solitons, soliton and vortex clusters predicted here may be realized in experiments in nonlinear optics and Bose–Einstein condensates by means of the state of-the-art technologies. [ABSTRACT FROM AUTHOR]