We present the first experimental demonstration of a multiple-radiofrequency dressed potential for the configurable magnetic confinement of ultracold atoms. We load cold $^{87}$Rb atoms into a double well potential with an adjustable barrier height, formed by three radiofrequencies applied to atoms in a static quadrupole magnetic field. Our multiple-radiofrequency approach gives precise control over the double well characteristics, including the depth of individual wells and the height of the barrier, and enables reliable transfer of atoms between the available trapping geometries. We have characterised the multiple-radiofrequency dressed system using radiofrequency spectroscopy, finding good agreement with the eigenvalues numerically calculated using Floquet theory. This method creates trapping potentials that can be reconfigured by changing the amplitudes, polarizations and frequencies of the applied dressing fields, and easily extended with additional dressing frequencies.