The dynamic gain of a few-mode erbium-doped fiber amplifier (FM-EDFA) is vital for the long-haul mode division multiplexing (MDM) transmission. Here, we investigate the mode-dependent dynamic gain of an FM-EDFA under various manipulations of the pump mode. First, we numerically calculate the gain variation with respect to the input signal power, where a mode-dependent saturation input power occurs under different pump modes. Even under the fixed intensity profile of the pump laser, the saturation input power of each spatial mode is different. Moreover, high-order mode pumping leads to a compression of the linear amplification region, even though it is beneficial for the mitigation of the differential modal gain (DMG) arising in all guided modes. Then, we develop an all-fiber 3-mode EDFA, where the fundamental mode of the pump laser can be efficiently converted to the LP₁₁ mode using the all-fiber mode-selective coupler (MSC). In comparison with the traditional LP₀₁ pumping scheme, the DMG at 1550 nm can be mitigated from 1.61 dB to 0.97 dB under the LP₁₁ mode pumping, while both an average gain of 19.93 dB and a DMG of less than 1 dB can be achieved from 1530 nm to 1560 nm. However, the corresponding signal input saturation powers are reduced by 0.3 dB for the LP₀₁ mode and 1.6 dB for the LP₁₁ mode, respectively. Both theoretical and experimental results indicate that a trade-off occurs between the DMG mitigation and the extension of the linear amplification range when the intensity profile of pump laser is manipulated.