With a child who takes strattera, (atomoxetine) what happens if you gradually give a bigger and bigger dose over a few months?

Not sure of question. Routinely, a family would work with the doctor, starting with a low dose of strattera (atomoxetine) and increasing it slowly over time until either you get the benefit you're seeking or unacceptable side effects appear. Side effects typically happen first, then fade over time; benefits appear more slowly but last. Finding the optimal balance can take time but is worth it when it works (about 45% of cases).
Do not increase med. You should never increase any medication without consulting the prescribing physician. Strattera (atomoxetine) can be gradually increased in a child or adult to help with adhd symptoms as long as the individual is tolerating the strattera (atomoxetine). However the highest recommended dosage is 100mg.