Can you lay
parquet over
an existing floor?

Sure. If you put down a floating floor the affirmative answer is clear to see. But even gluing a new floor onto an old one is a viable option in the vast majority of cases. Just make sure that all the simple technical rules of perfect gluing are followed and the new parquet will adhere solidly to the old one, and give your home a brand new and natural look. If you use engineered parquet, the thickness of the planks will remain minimal and it will be much easier to fit and adjust the floor to where the doors, even armoured doors, swing open.