In 5G and beyond networks, efficient scheduling is essential to exploit the gains of multi-user MIMO (MU-MIMO) equipped with carrier aggregation and joint transmission (JT). However, cross-cell and cross-carrier scheduling under QoS constraints is challenging due to the strong coupling across users, base stations, and carriers. In this work, we address this problem in multi-cell MU-MIMO networks to maximize system throughput for both JT and non-JT users under rate constraints. The optimization is highly complex as scheduling variables and beamforming (BF) vectors are intertwined. To tackle it, we propose an approximate but tractable surrogate by leveraging the eigen-based zero-forcing BF and massive MIMO asymptotics. The reformulated problem has a separable structure and is amenable to efficient solutions by a penalty-based block coordinate descent method. Simulations demonstrate that the proposed scheduler not only meets the QoS requirements well but also achieves remarkable throughput gains over existing schemes.