To do this you need to run cloning software on your machine and not depend on the limited abilities of a duplicator. However, the C: drive Partition should be expanded to take up all of the available space on the new 2 TB unit. that will never be changed) should be the same on the resulting larger HDD. More specifically, any "hidden" system Partitions (things that contain backups, a recovery Partition, etc. I suspect what you want is that the Partitions on the original 500 GB unit should be reproduced in some cases, and upgraded for others.
The result is that the clone copy you make will be exactly the same as the original in all aspects, including the sizes of all the original Partitions. Most stand-alone duplicators can do cloning, but have no real smarts or options you can customize. The problem originates in your choice of cloning system.