Adding more layers to a neural network leads to a larger number of parameters to train. As a consequence, the network also requires more training samples or stronger regularization methods. Otherwise, overfitting will become a problem. The network will become too complex for the (relatively) small amount of training data.

Having said that, a reason to add more layers is to increase exactly that complexity of the network. If you think your task requires very complex functions and the only way to incorporate such functions into your neural network is to add more layers, then you have a good reason to add more layers. However, the amount of available training data and the network complexity still need to match/work together.

Start with one hidden layer in the neural network and then go deeper and increase the number of hidden layers one by one , as long as the output response of the neural network is getting better.

https://arxiv.org/pdf/1404.7828)

https://www.freecodecamp.org/news/want-to-know-how-deep-learning-works-heres-a-quick-guide-for-everyone-1aedeca88076/