Materials with open porosity are known to absorb sound very well. However, their efficiency in acoustic absorption and insulation is sometimes restricted to specific frequency ranges. It is possible to circumvent this drawback by designing a porous microstructure that can be modified on the fly and thereby enabling the change in its crucial geometrical parameters like tortuosity that influence the intensity of viscous energy dissipation phenomena taking place on the microscale. A prototype of such a material consisting of relocatable small steel balls embedded in a periodic rigid skeleton is devised and additively manufactured in separate pieces in the stereolithography technology. The balls are inserted into proper places manually. The full sample is then assembled and its acoustic characteristics are determined computationally and experimentally using dual-scale, unit-cell analyses and impedance-tube measurements, respectively. The resulting material is shown to possess two extreme spectra of normal incidence sound absorption coefficient and transmission loss that are dependent on the particular position of balls inside the microstructure. In consequence, acoustic waves from a much larger frequency range can be effectively absorbed or insulated by a relatively thin material layer compared to a similar design without movable balls.