Can we use feature selection and dimensionality reduction together?
Every time you compress the feature space you are losing some information. The original feature engineering stage you outlined sounds like a meaningful compression &amp; might make sense in the context of your problem. The second compression on the other hand might only serve to lose some information.
I would only perform the second compression if the classifier you are training is struggling resource-wise to train your model after the initial compression. In this case you might want to sacrifice some information to train the model quicker. But this step should only be investigated after you try training your model with only the original compression &amp; are not satisfied with the speed of training.
Good luck!