Existing works on cell-free systems consider either coherent or non-coherent downlink data transmission and a network deployment with a single central processing unit (CPU). While it is known that coherent transmission outperforms non-coherent transmission when assuming unlimited fronthaul links, the former requires a perfect timing synchronization, which is practically not viable over a large network. Furthermore, relying on a single CPU for geographically large cell-free networks is not scalable. Thus, to realize the expected gains of cell-free systems in practice, alternative transmission strategies for realistic multi-CPU cell-free systems are required. Therefore, this paper proposes a novel downlink data transmission scheme that combines and generalizes the existing coherent and non-coherent transmissions. The proposed transmission scheme, named mixed transmission, works based on the realistic assumption that only the access points (APs) controlled by a same CPU are synchronized, and thus transmit in a coherent fashion, while APs from different CPUs require no synchronism and transmit in a non-coherent manner. We also propose extensions of existing clustering algorithms for multi-CPU cell-free systems with mixed transmission. Simulation results show that the combination of the proposed clustering algorithms with mixed transmission have the potential to perform close to the ideal coherent transmission.