Check for RAID first. This will impact how you setup the new drive(s) to clone to. Hopefully (since it's a server...and a domain controller)...it's on RAID. If it is a server running on just one hard drive (lol at the guy that set that up)...it's pretty much the same as a desktop computer..except the cloning/partitioning software you use may not want to install on a server (so which tool(s) you use will be a whole 'nother subject).
If it IS RAID....your choices on doing this will vary. Hopefully it's a decent server with a good RAID controller that allows you to replace drives and do an online expansion...creating lots of new free space on the volume..and then you can use diskpart (built into Windows) or 3rd party tools to increase partition space. However only certain tools will deal with the %system% partition.
Depending on the RAID controller...you may have options to improve things on this server. Since you mention one hard drive...I'm going to assume it's a RAID 1 or a RAID 5...if it's RAID. For a small business...it's tolerable that way. If it's a larger business...or growing..and the server isn't too zippy....this is why. I usually do a RAID 1 for the OS, and another RAID 1 for the data...(smaller business)...or RAID 5 or 10 for the data (larger business, databases, etc). Much better performance since it's 2x spindles to the OS and you can span the pagefile across them. So depending on what options and tools you have, you can take a single volume with 3x partitions and spread it across two volumes with multiple partitions and end up with a better overall server.
