Space division multiplexing (SDM) systems using few-mode fibers (FMF) are essential for next-generation fiber optic communications. Optical amplifiers with low noise, minimal differential modal gain (DMG), and minimal differential spectral gain (DSG) are essential for these systems. In this work, we present a method to design and optimize a two-stage few-mode erbium-doped fiber amplifier (FM-EDFA) using a joint DMG-DSG minimization approach. This methodology involves the pumping profile design and the gain flattening filter design. Simulation results show the two-stage FM-EDFA achieves DMG and DSG below 2.8 dB and 0.42 dB, respectively, with an optical signal-to-noise ratio above 19 dB across the C-band, enabling a system capacity of 48.6 Tbps. This work reveals the effectiveness of this two-stage FM-EDFA for optical amplification in the context of SDM systems. (c) 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement