Could a body produce too much blood?

Yes.: In some instances, a person may produce too many red blood cells. An example of a disease like this is polycythema vera. This is an abnormal bone marrow condition (a myeloproliferative disorder) in which the patient's bone marrow makes too many red blood cells. Another reason for the bone marrow to make excess red blood cells is chronic hypoxia (low oxygen) in association with COPD or apnea.