Interference alignment (IA) has been a powerful approach to achieve the maximum degree of freedom (DoF) for K users multiple-input-multiple-output (MIMO) interference channels. However, due to the feasibility constraint, aligning all the interference signals at each receiver is impractical for large K without symbol extension. In this paper, we propose two best-effort interference alignment (BEIA) schemes that the network selects the maximum number of interfering transmitters to align their signals given the feasibility conditions when each transmitter-receiver pair has a constant number of data streams. Besides, in case of not all interfering signals aligned at each receiver, an upper bound of the average throughput is derived. Simulation results show that the proposed schemes have superiority over the traditional methods, such as time division multiple access (TDMA) and cluster IA(CIA), in low and moderate signal-to-noise ratio (SNR) region in terms of average user throughput. In addition, the proposed max-min relative interference distance alignment scheme outperforms the proposed scheme of equal interfering transmitters number alignment in terms of both average user throughput and minimum user throughput.