How to incorporate features available only at training time into my model

I’m building classifier with a binary label.
In my particular dateset the training data has many more features than the test set, in fact most of them are not available in the test set (beyond my control).
How can I still utilize those features when training my model? It’ll be a shame to just throw them away.
I thought of maybe trying to predict the training-only features as well as the labels, sort of like semi supervised learning.
Most of the missing features are categorical.