An all-fiberized and narrow-bandwidth master oscillator power amplification (MOPA) system with record output power of 4 kW level and slope efficiency of 78% is demonstrated. Tandem pumping strategy is tentatively introduced into the narrow-bandwidth MOPA system for thermally induced mode instability (TMI) suppression. The stimulated Brillouin scattering (SBS) effect is balanced by simply using one-stage phase modulation technique. With different phase modulation signals, SBS limited output powers of 336 W, 1.2 kW and 3.94 kW are respectively achieved with spectral bandwidths accounting for 90% power of ${\sim}$0.025, 0.17 and ${\sim}$0.89 nm. Compared with our previous 976 nm pumping system, TMI threshold is overall boosted to be ${>}$5 times in which tandem pumping increases the TMI threshold of ${>}$3 times. The beam quality ($M^{2}$ factor) of the output laser is well within 1.5 below the TMI threshold while it is ultimately saturated to be 1.86 with the influence of TMI at maximal output power. Except for SBS and TMI, stimulated Raman scattering (SRS) effect will be another challenge for further power scaling. In such a high power MOPA system, multi-detrimental effects (SBS, SRS and TMI) will coexist and may be mutual-coupled, which could provide a well platform for further comprehensively investigating and optimizing the high power, narrow-bandwidth fiber amplifiers.