A new design of supercontinuum-generating microstructure fibers is demonstrated, with supercontinuum emission produced in six submicron-diameter cores surrounding a larger central core with a diameter of 2 to 5 m. Such a multiple-core microstructure-fiber design not only allows the total energy of supercontinuum emission to be increased, but also offers a practical way of fabricating microstructure-integrated bundles of small-core high-index-step fibers with very large lengths. Submicron-core fused-silica microstructure fibers are shown to provide maximum ratios of the fiber-core-confined laser power to the fiber-core diameter, allowing limiting waveguide enhancement factors to be approached for a broad class of nonlinear-optical processes contributing to supercontinuum generation. PACS 42.65.Wi; 42.81.Qb