Be careful about mixing medications, whether prescribed or over the counter. It could be dangerous. Always check with your doctor or pharmacist.

An article in Science Daily talks about one example, combining Ibuprofen and aspirin:

High risk patients taking aspirin and ibuprofen were around nine times as likely to have heart attacks and strokes over one year as those on lumiracoxib.

This is especially true if you suffer from osteoarthritis. NDTV Blog adds:

A study published in the Annals of the Rheumatic Diseases (APRIL 2007) says that ibuprofen may increase the risk of congestive heart failure and blood clots in high-risk patients with osteoarthritis who take aspirin. Osteoarthritis is the most common form of arthritis, usually occurring after middle age, marked by chronic breakdown of cartilage in the joints leading to pain, stiffness, and swelling.