In complex colloidal systems, interparticle interactions strongly affect the dynamics of the constituting particles. A study of the dynamical response also provides invaluable information on the character of those interactions. Here we demonstrate how tuning the electrostatic interactions by an ionic surfactant in dispersions of magnetic nanoplatelets leads to developing new dynamic modes in magnetic response spectra. The collective modes can be induced or suppressed by either varying the concentration ratio of the magnetic nanoplatelets (MP) to the surfactant or increasing the MP concentration reflecting the nanoscale characteristics of this fluid magnet.