Any way to add 4K support to a late 2012 iMac?
Your model iMac offered three graphics card options:


NVIDIA GeForce GTX 660M
NVIDIA GeForce GTX 675MX
NVIDIA GeForce GTX 680MX


In terms of graphics memory these cards provided 512MB, 1GB and 2GB respectively.

Strictly speaking all these cards are capable of a maximum digital resolution of 4,096 x 2,160. However, your model iMac was only capable of 2,560 x 1,440 internal resolution, and up to 2,560 x 1,600 for external displays.

I'm not sure for the exact reason of the apparent discrepancy, so I can't guarantee there'd be absolutely no way to achieve what you want. However, I very much doubt it'd be economical to achieve.