Is is possible to make a full flush toilet from an American Standard Cadet 3. The toilet is on a septic system and does not have the power to move waste all the way to the septic tank.

There could be blockage, get a system inspected to get the correct view of the system. Call a septic service or local authorities for running water test and drain field inspection.
It is very important to have your system inspected every two to three years, do not flush grease and other non biodegradable substance into the toilet.
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If your toilet is not moving waste all the way to the septic, then there may be a blockage in the waste line or it may not be plumbed correctly. There is no reason why you should not be able to make a full flush on septic. I have live on septic for many years and it should flush as well as living in the city. Is your water supply nice and strong? This sound like a gravity issue with the waste line or a blockage, If you can get under your house and see how the waste line is run, that would be helpful, it should be aimed straight down underneath your toilet and never running uphill at any point on the way to the septic tank. Also is there a vent in the waste line at the proper distance. If not, that could also be the issue. Good luck. P.s. does your septic tank need pumped out?