Graphic Card Replacement to GT 750M - How? Options?

Sadly there is no means to replace the graphic services (GPU) in this series. This model uses Intel's Haswell CPU which has an integrated GPU subsystem (Intel Iris Pro graphics processor). Here is an image of your logic board: 21.5" iMac Logic board. The Red colored box is the Haswell chip, the little chip on the carrier is the GPU chip.

But! There is a way you can use an external case which hosts a GPU card and then connects to an external monitor in a daisy chain config. I don't recommend doubling back the signal to the internal display as your system is only Thunderbolt not Thunderbolt2. That is if you are using your system for gaming or video editing.

Here's one company that offers a workable solution: Bizonbox.

You'll need to save the pennies here to buy it. Or, look at upgrading your system to a newer model that has the needed performance (selling yours and getting a used system)

Sorry still can't replace it ;-{

The model you have was not as popular and was short lived. Here's an image of your logic board:

The green chip in the middle is the NVIDIA GT750m GPU chip which is soldered onto the logic board and not removable. The four other chips around it is the video RAM.