External eGPU for iMac (Retina 5K, 27-inch, Late 2014)

A 2014 27" iMac is too old to support an EGPU, please refer to Use an external graphics processor with your Mac - Apple Support

One of the minimum specifications is the iMac must have a Thunderbolt 3 port, a 2014 does not have this and no that cannot be upgraded. If you want an iMac with Thunderbolt 3 I think you will need a 2017-2020 27" iMac.

That Mac only has Thunderbolt 2 ports.

Apple does sell a bi-directional Thunderbolt 3-to-2 converter - but the amount of data that you can put through it will be bottlenecked by the speed of the slowest (Thunderbolt 2) side. That would probably make using an eGPU impossible or impractical even if there were no other (software / driver) issues.

As I recall, Thunderbolt-3-based eGPUs were rather expensive and limited in selection. It might be best to save the money you would have spent on an eGPU and put it towards the eventual purchase of an Apple-Silicon-based Mac. With the Apple Silicon Macs, you tend to get more GPU cores as you go up in a particular generation from the base chip, to the Pro chip, to the Max chip.

Software: Apple does not provide native Thunderbolt-2 eGPU support. Some sort of third party / open source kernel patch/extension software will be required.

Hardware: For an enclosure I would suggest either Akitio Node Titan (least expensive option still sold new), the Razer Core X (physically larger, good if you need the extra card length, bad if you need desk space), or the Sonnet Breakaway Box (what I've been using with a 2018 mini since 2019). For compatibile graphics cards see the link everyone else has already shared for the OS you have installed (Use an eGPU with your Mac - Apple Support). I'd suggest an RX 5500XT/5600XT/5700/5700XT. The 6800/6800XT might be an option if you only need to use Big Sur, but those cards are frequently built too long to fit inside an eGFX enclosures, so double check card length vs maximum enclosure size.

Performance Notes: eGPUs work best with external monitors directly connected to the GPU. Rendering to the internal display will have a performance penalty that scales with frame rates, and this penalty is notably worse on TB2 (16GBps PCIe 2.0x4) than on TB3 (22-32GBps) so performance improvements will not be as great as expected from PC performance numbers. Also the open source kernel patches may require disabling system integrity protection making for a performance/security trade off.

Only Thunderbolt 3 equipped Mac's from 2017 and later supported eGPU's.

see > Use an external graphics processor with your Mac - Apple Support

Per this Apple article, your iMac must have ThunderBolt 3 ports to use Apple's GPU support:

Use an external graphics processor with your Mac - Apple Support

A Late 2014 has ThunderBolt 2. T3 ports in iMacs did not appear until the 2017 models.

There may be third-party workarounds.

Gotcha, while your 2014 may be working just fine today, please consider it is obsolete meaning it cannot (and will never be able to) run current versions of Mac OS AND it's 10+ years old and could fail tomorrow. In addition the longer you keep it up and running the less compatible it will be with new software. Where I am going with this is train of thought is have you considered just buying a new Mac? Please note I DID NOT say another iMac. Current Mac Mini's are orders of magnitude faster and can run current versions of Mac OS. For about $1500 USD you can have a brand new iMac and a display that has the same qualities as your current 11 year old system that will be faster, more compatible with current apps and could very well work for another 10+ years.

If you want another external display (I think you are saying you want 2 displays with similar specifications) you can buy an Apple Studio Display ($1599) or the Samsung 27" display with similar spec to the Apple Studio Display. I've seen those as low as $699.

Your 27” Late 2014 Retina 5K iMac does not have the ability to drive another 5K display.

iMac (Retina 5K, 27-inch, Late 2014) - Technical Specifications - Apple Support

”Simultaneously supports full native resolution on the built-in display and up to 3840 by 2160 pixels on an external display”