Is it possible to add a second physical hard drive without introducing a new drive letter?

What I would do instead is buy the biggest drive you can afford, make that your primary drive and move everything from the old drive to the new one using an image tool. Trying to merge physical drives into a single drive letter without making use of a raid array is difficult and prone to errors and failures. Not to mention if your primary disk fails you will permanantly loose all data on both drives. The second drive cannot be used by itself once it's linked to your older primary drive.

you can use junction to create directory symbolic links.