The design of network-wide schemes requires computationally efficient traffic models. The Macroscopic Fundamental Diagram (MFD) is a promising tool for such an application. Unfortunately, current semi-analytical approaches require an inaccurate network reduction to a corridor. Our methodology allows us to estimate the MFD for general networks, without the information loss induced by the reduction of networks to corridors. The model is based on the method of cuts, but can account for different demand patterns, and determine the upper bound of network flow. Thereby, we consider flow conservation and the effects of spillbacks at the network level. Furthermore, we propose an overall framework which decomposes the network into a set of corridors, and then applies our model to each of them while taking into account the dependencies across corridors (e.g. due to turning flows and spillbacks). Aggregating the results leads then to a network MFD. The proposed framework applies to any general network, and we show a proof of concept using a simple but sufficient case study. We compare the results to the original method of cuts, and a ground truth derived from a microscopic simulation. Analysis reveals a strongly reduced error of the estimated MFD based on our method, compared to the currently applied approach. The potential of this methodology lies in its implementation simplicity and reduced computational cost.