Find out the name or the index of the layer you need to get the results for and make a new model considering the output of that layer.
A model that outputs only that layer:
earlyPredictor = Model(cnn.inputs, cnn.layers[theIndexYouWant].outputs)
#alternatively
earlyPredictor = Model(cnn.inputs, cnn.get_layer(theNameYouWant).outputs)
A model that outputs both the final output and the desired layer:
fullPredictor = Model(cnn.inputs, [cnn.output, cnn.layers[index].output])
The difference between using "output" and "outputs" only appear when a layer or model has more than one output. The second example would need extra care to concatenate the result lists if the cnn output and the specific layer output are multiple.