Monarch

Monarchies take a wide variety of forms, such as the two co-princes of Andorra, positions held simultaneously by the Roman Catholic Bishop of Urgel (Spain) and the elected President of France (although strictly Andorra is a diarchy). Similarly, the Yang di-Pertuan Agong of Malaysia is considered a monarch despite only holding the position for five years at a time.

Question: can you have a president and a monarch
Answer: yes