We analyze the performance of massive MIMO systems with N-antenna users, The benefit is that N streams can be multiplexed per user, at the price of increasing the channel estimation overhead linearly with N. Uplink and downlink spectral efficiency (SE) expressions are derived for any AT, and these are achievable using estimated channels and per-user-basis MMSE-SIC detectors. Large-system approximations of the SEs are obtained. This analysis shows that MMSE-SIC has similar asymptotic SE as linear MMSE detectors, indicating that the SE increase from having multi-antenna users can be harvested using linear detectors. We generalize the power scaling laws for massive MIMO to handle arbitrary N, and show that one can reduce the multiplication of the pilot power and payload power as 1/M where M is the number of BS antennas, and still notably increase the SE with M before reaching a non-zero asymptotic limit. Simulations testify our analysis and show that the SE increases with N. We also note that the same improvement can be achieved by serving N times more single-antenna users instead, thus the additional user antennas are particular beneficial for SE enhancement when there are few active users in the system.