Multiple cation-substitution is an effective method to improve the stability of organic-inorganic hybrid perovskite thin-films. Here, we apply this approach to quasi two-dimensional (quasi-2D) perovskite materials, and investigate the effect of Cs and K doping on the performance of quasi-2D perovskite LEDs (PeLEDs). It is found that Cs significantly reduces the efficiency roll-off of quasi-2D PLEDs at high current density, which leads to a high current efficiency (CE) - even at an operation current density as high as 1000 mA cm-2. In addition, the incorporation of a small amount of K further increases the device quantum efficiency thanks to its passivation effect. As a result, our green PeLED, which is based on a multi-cation quasi-2D perovskite, reaches a brightness of 45 600 cd m-2, and a maximum CE of 22.5 cd A-1. The approach introduced in this work has great potential to enhance the performance of quasi-2D perovskite light-emitting diodes.