The Medford Mail Tribune reports that two of the fires were lit in piles of trash in one alley.
Medford police are encouraging the public to come forward with any information on the person or persons starting the fires or be on the lookout for suspicious activity. Department officers are also on the lookout.
Medford Fire-Rescue battalion chief Rick Rohrbough says whoever is starting the fire is "getting everybody ramped up."
On Saturday, as fire fighters were dousing the blazes in the trash piles, the third fire began smoking near them. That fire burned the outside wall of a building.
While Saturday's fire was minor, one of three fires set July 15 was set outside of an occupied home. The woman inside was uninjured. Police also believe that arsons may have started a massive fire that leveled a former fruit-packing plant.