If you start combining several composite nodes in your Node view, it is important to understand how they work if you want to get the desired result.
There is a specific order in which you should set your Composite nodes. Each time you process images through a 3D Flat Composite node, the images will be merged together. Images processed in later Composite nodes cannot be inserted between images of the previous composite since it is a flat image.
If you used Pass-Through type Composite nodes in your network, the images will not be processed together before the final Composite. It is important to keep your final Composite as a 3D Flat Composite in order to read the layer ordering correctly.
The most efficient networking system for obtaining the desired result is likely the Pass-Through composite mode throughout the whole network. This way, you can create individual compositions to keep your network clean and organized, but process everything together at the end.