Is it possible that the oil is really dirty and you are just adding new oil to dirty oil? Running with dirty oil will cause high oil consumption, also running with dirty oil will cause the piston rings to stick and consume oil. If the oil is dirty, get it changed and see if that helps the oil consumption. If you are driving hard, it would be normal to use a quart in 1000 miles but that's still a little high. If the engine has been overheated, it's possible that the piston rings are collapsed which would cause high oil consumption. I recommend you check your oil more often than 1500 to 2000 miles, check it every time you fill the gas tank because you're going to run out of oil and ruin the engine if it consumes oil and you don't check it until it needs 2 quarts..
Sorry I should have given more background. About 8 months ago I noticed smoke from the exhaust on cold starts. I immediately took it to the dealer (where it's been serviced regularly since purchase) and was told it was nothing more than condensation. A couple months later, and after several checks for the same complaint, it needed a ignition switch. When that was replaced they said the oil level was fine. A week later I took it back for the same smoke complaint. They told me there was no oil in the engine. One week and 100 miles after they said all was fine. They told me it would cost up to $5000 to repair with no guarantee it would be fixed. That they really didn't know what was causing the loss of oil. I do check the oil every other fill up and top off as needed, the 1500 miles was just an estimate. The oil is also changed every 3000 miles or so. I do use full synthetic. There are 95,000 miles on the vehicle and I'd really like to keep it going for at least another 60K. Any other ideas? Thanks for your response.