Can an external hard disk be virtually merged with C drive?

My problem is that I have a computer with 1TB internal HDD (C drive) and various programs derive links from corresponding folders in that drive.
Now I wish to run the same programs from my another computer with 500GB HDD (C drive). To accommodate the data I have to attach an ext hard disk with 500 GB to supplemnt the capacity. But the ext hard disk takes the drive letter some E or F and the links for the programs do not work. Is there any way or trick to make the OS virtually recognise or deem the the ext hard disk as part of C drive? .
-Rama Reddy Karri
 
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