We present a multi-region extension of standard power-law background subtraction for core-level EEL spectra to improve the robustness of background removal. This method takes advantage of the post-edge shape of core-loss EEL edges to enable simultaneous and co-dependent fitting of pre- and post-edge background regions. This method also produces simultaneous and consistent background removal from multiple edges in a single EEL spectrum. The stability of this method with respect to the fitting energy window is also discussed.