2) that the infection resides elsewhere
in the body, such as an abscess
in the heart or even
in the lungs, and is recurrently ‘seeding’ bacteria to the lungs; and 3) that the pneumonia is a non-infectious process, which is much less likely.
At this point, it would be wise to consult with a pediatric infectious disease specialist. This might be a time to hold the antibiotics and repeat comprehensive blood and urine cultures.