You can exchange the (MXM3) GPU in the iMac9,1 with 2.93 GHz and 3.06GHz CPU with a modern metal AMD GPU - both models were equipped with an MXM3 slot.[br]
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The process and source of compatible graphics card video BIOS (aka vBIOS) versions necessary has been described on this [link|https://forums.macrumors.com/threads/2011-imac-graphics-card-upgrade.1596614/post-31995643|post|new_window=true]. You will loose the EFI Boot screen, but can use [link|https://dortania.github.io/OpenCore-Legacy-Patcher/|OCLP|new_window=true] to enable an OpenCore emulated boot picker and more importantly can install and run more recent macOS versions on this iMac9,1 model.[br]
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The process and source of compatible graphics card video BIOS (aka vBIOS) versions necessary has been described on this [link|https://forums.macrumors.com/threads/2011-imac-graphics-card-upgrade.1596614/post-31995643|post]. You will loose the EFI Boot screen, but can use [link|https://dortania.github.io/OpenCore-Legacy-Patcher/|OCLP] to enable an OpenCore emulated boot picker and more importantly can install and run more recent macOS versions on this iMac9,1 model.[br]
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You need some patience, tools, a rainy Sunday...[br]
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P.S.:[br]
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To complete the answer: You can also re-use original Apple MXM cards from iMac11,x-iMac12,x models. Unfortunately these systems use a different encoding (eDP) to drive the internal display and thus all vBIOS versions from those cards are not compatible with the iMac9,1 (LVDS). Only cards from the iMac10,1 21.5 (LVDS) can be re-used without flashing a different vBIOS. [br]
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You can cross flash the iMac9,1 4850 vBIOS and the iMac10,1 21.5 ATI 4670 vBIOS onto the same cards from iMac10,1 27", iMac11,1 and iMac11,2 models (all eDP) to make the fully compatible. Physically these cards are identical. [br]
You can exchange the (MXM3) GPU in the iMac9,1 with 2.93 GHz and 3.06GHz CPU with a modern metal AMD GPU - both models were equipped with an MXM3 slot.[br]
[br]
The process and source of compatible graphics card video BIOS (aka vBIOS) versions necessary has been described on this [link|https://forums.macrumors.com/threads/2011-imac-graphics-card-upgrade.1596614/post-31995643|post|new_window=true]. You will loose the EFI Boot screen, but can use [link|https://dortania.github.io/OpenCore-Legacy-Patcher/|OCLP|new_window=true] to enable an OpenCore emulated boot picker and more importantly can install and run more recent macOS versions on this iMac9,1 model.[br]
[br]
You need some patience, tools, a rainy Sunday...[br]