Yes you can upgrade the HD to a 4 TB disk IFIXIT HD replacement guide
But you do have an issue here that you may need to deal with depending on the HD you put in. This is the first generation of systems that Apple started using the internal thermal sensors of the drives (using modified HD firmware via the power connector).
Depending on the HD you get you may need to either apply some software to over-ride the systems cooling system or splice in an external sensor (B&W wires) to the power harness cable. So the fans don't run wild as the HD sensor input would be missing. Some of the newest drives now work correctly without any add-on software or modifications.
Another option here is to add-in a second, yes I did say second HD using the IFIXIT 2nd drive kit. While you'll need to use the smaller laptop type of HD you won't need to deal with the thermal sensor. Or it you really want some speed you could put in a SSD here while you have it opened up.
Yes. Here are some that will work for you: http://eshop.macsales.com/shop/hard-driv...
1 TB (7200 RPM) Int. HD Interface: Serial ATA (6 Gb/s*)
Details: *As shipped, these models only supported the 3 Gb/s Serial ATA 2.0 standard for both a 3.5" hard drive and a 2.5" SSD. However, as first discovered by OWC, the iMac EFI Update 1.6, released two days later, quietly provided 6 Gb/s Serial ATA 3.0 support.
Your drive may also be covered under warranty if it has failed. Enter your serial number here to find out: http://www.apple.com/support/imac-harddr...