Good morning AstroNOT. I apologize for the delay in my response to this issue.

Does the game crash when no other programs are running in the background? Furthermore, please be sure that any anti-virus software you have has the appropriate exceptions for Final Fantasy XIV. Lastly, please disable Full Screen Optimizations to see if this may make a difference. To disable this feature, please find the "ffxiv_dx11.exe" and right click it and select properties. Then under the compatibility tab, there will be a check box labeled "Disable Full Screen Optimizations". Check it and click apply.

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