Based on the information available, I found that Lipitor, a medication used to treat high cholesterol, is typically compatible with blood thinners. However, it's crucial to consult a healthcare professional before combining any medications. Here are some blood thinners that, in general, can be used with Lipitor:

1. Warfarin (Coumadin): This is an anticoagulant that can be taken with Lipitor. However, patients need to be closely monitored due to the increased risk of bleeding [1].

2. Clopidogrel (Plavix): This antiplatelet drug can be used with Lipitor. It's often prescribed after certain types of heart procedures [1].

3. Aspirin: Aspirin is another blood thinner that can be used with Lipitor. It's often recommended for patients at risk of heart disease [1].

4. Prasugrel (Effient): This antiplatelet drug can be used with Lipitor, especially in patients with acute coronary syndromes [1].

5. Ticagrelor (Brilinta): This antiplatelet drug can be used with Lipitor, particularly in patients with acute coronary syndromes [1].

6. Apixaban (Eliquis), Rivaroxaban (Xarelto), and Dabigatran (Pradaxa): These newer oral anticoagulants are not typically used with Lipitor due to the increased risk of bleeding [2].

Remember, it's essential to consult a healthcare professional before starting or changing any medication regimen. They can provide personalized advice based on your health history and current medications.

Sources:
[1] "Lipitor (atorvastatin) Drug Interactions." RxList, www.rxlist.com/lipitor_atorvastatin/drug-interactions.htm.
[2] "Blood Thinners and Statins." Drugs.com, www.drugs.com/article/blood-thinners-and-statins.html.
[3] "Lipitor (Atorvastatin)." DrugPatentWatch, www.drugpatentwatch.com/drugs/lipitor.

Note: This information is a general guide and not a substitute for medical advice.