A material platform of multilayered surface-plasmon-dielectric-polariton systems is introduced, along with a new physical mechanism enabling simultaneous cancellation of group-velocity and attenuation dispersion to extremely high orders for subwavelength light of any small positive, negative, or zero group velocity. These dispersion-free systems could have significant impact on the development of nanophotonics, e.g., in the design of efficient and very compact delay lines and active devices. The same dispersion-manipulation mechanism can be employed to tailor at will exotic slow-light dispersion relations.