Chemotherapy Regimes

Has anyone ever heard of a chemotherapy regimen (3 cycles) being modified (increased dosage of medication), because a patient tolerates the first round?

Yes. Sometimes, the first doses of drugs are low, because these drugs can be toxic. Not only chemotherapy, antibiotics and some others too. The doses are usually calculated from body weight and kidney and liver, but there is usually the maximum, minimum and first dose levels to protect against overdose and adverse effects.
chemo drugs can be particularly dangerous because they are designed to kill cells. at right, they kill most cancer cells. but if the levels in the blood is too high, they kill indiscriminately, usually causing a small number of blood cells and other toxic effects. After one lap, blood and observation indicate if the doses are adjusted. I would not be surprised to see the change in dose. A dose increase indicates that the initial dose was not high enough to ensure the optimal effect against cancer.
Another reason for the change of regime would be if the patient does not tolerate drugs, such as effects of an allergy or sever side, but that would mean changing the drugs themselves, and not the dosage.

Yes. Depends on how you tolerate the chemotherapy. It may be amended or another, up or down.

Yes, it happened to my aunt. It tollerated well, and they wanted to deal more aggressively if they could. They increased the dosage for the third cycle.