Answer:
In most cases - it is not possible (or desirable), & in few cases cases, it might be possible (or desirable).
Step-by-step explanation:
Profession is an occupation based on proper formal qualification, training. Eg : Doctors, Lawyers.
They require specialised knowledge (accredited) to practice as a professional. So, involvement in multiple professions is not possible (desirable) in most cases, as it hinders focus & specialised competence (expertise) in single field.
However, in some cases, it might be possible (desirable) if the fields are related. And it also might be need of exposure for the professional. For eg - An economist might be economic consultant & a professional teacher in an education organisation at the same time.