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Based on the available information, yes, Lipitor (atorvastatin) can increase warfarin-related side effects.

Warfarin is an anticoagulant medication that works by slowing down the blood clotting process [1]. Lipitor, on the other hand, is a statin medication used to lower cholesterol levels [2]. According to the drug interactions information from Drugs.com, when Lipitor is taken with warfarin, it can increase the blood-thinning effects of warfarin, which can increase the risk of bleeding-related side effects [3].

The National Center for Biotechnology Information (NCBI) published a case report of a patient who experienced an international normalized ratio (INR) increase after starting Lipitor, which was managed by reducing the warfarin dose [4]. INR is a standardized way of measuring how long it takes for a person's blood to clot, and an increased INR indicates a higher risk of bleeding.

Therefore, healthcare providers should monitor patients taking both Lipitor and warfarin closely for signs of bleeding and adjust the warfarin dose as necessary [3]. Patients should also inform their healthcare providers of any new medications or changes in medication, including starting or stopping Lipitor [3].

In summary, based on the available information, Lipitor can increase warfarin-related side effects by increasing the blood-thinning effects of warfarin, which can increase the risk of bleeding-related side effects.

Sources:
[1] <https://www.ncbi.nlm.nih.gov/books/NBK537202/>
[2] <https://www.drugpatentwatch.com/p/tradename/LIPITOR>
[3] <https://www.drugs.com/drug-interactions/lipitor-with-warfarin-276-128-2311-0.html>
[4] <https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8861410/>