Lipitor (atorvastatin) is a medication used to lower cholesterol levels in the blood. According to MedlinePlus [3], the usual starting dose of Lipitor is 10-20 mg per day, which can be taken at any time of the day, with or without food. The dosage can be increased gradually, based on the individual's response to the medication and the doctor's recommendation. The maximum recommended daily dose of Lipitor is 80 mg [3].

A study published in the Journal of the American Heart Association [2] found that gradual titration of Lipitor, starting with a lower dose and increasing it over time, was associated with a lower incidence of muscle-related side effects compared to starting with a high dose. The study recommended starting with a lower dose of Lipitor and gradually increasing it to achieve the desired cholesterol-lowering effect, while monitoring for any side effects.

Drug Patent Watch [1] provides information on the different strengths of Lipitor available in the market, ranging from 10 mg to 80 mg. This suggests that Lipitor can be prescribed in different doses, including gradually increasing the dosage, as needed.

In conclusion, based on the provided sources, it is safe to say that Lipitor dosage can be gradually increased, based on the individual's response to the medication and the doctor's recommendation. Starting with a lower dose and gradually increasing it may help reduce the risk of muscle-related side effects. However, the maximum recommended daily dose of Lipitor is 80 mg. It is important to follow the doctor's instructions and report any side effects experienced while taking Lipitor.

Sources:
[1] https://www.drugpatentwatch.com/p/tradename/LIPITOR
[2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4613890/
[3] https://medlineplus.gov/druginfo/meds/a600045.html