Your system uses a custom SSD which is similar to the new M.2 SSD's.
Sadly, there is no 3rd party options in swapping out your SSD with a bigger unit at the present time and it is a very big job to even get to the SSD slot so that is not an option for you. Here's the details in an IFIXIT guide: iMac Intel 27" EMC 2639 SSD Replacement.
With that said, you still have a standard SATA connection on your logic board to mount a standard 3.5" HD unit. Here is the IFIXIT guide for getting to it: iMac Intel 27" EMC 2639 Hard Drive Replacement. As you can see this is likewise a big job and requires some special tools. In addition you will need the mounting brackets, screws and special cable harness; and lastly, the correct HD as Apple HD's use a special internal temp sensor to control the systems fans. I don't recommend putting an SSD Vs a HD. But I do recommend a newer SSHD unit which will give you some improved performance over a standard HD.
OK, so what to do?
First given the amount of work and collecting all of the needed pieces will be a bit of a job (so far I don't know of anyone who offers a hardware kit) I think you will want to let an authorized Apple service center do the work as the have better access to the parts and have the needed tools. I must warn you this maybe expensive! Do you really need to have the drive internally?
I would look at an external drive option using a Thunderbolt port connection. Frankly, a dual HD setup thats RAID'ed would be faster than most any internal HD you would put inside.
If you really wanted the internal HD I would think about selling your system and getting one that is better configured for your needs.