Short answer: Nope. Only option that is remotely close and I'm glad they did this is not receiving those messages in your email. -_- I checked the notifications list in the profile settings and turning off the respective games notifications won't fix it (Tested using my dummy and main accounts), nor will turning off the "messages from user" "friend requests" etc help, since these options only cover emails which was the only option in the settings. There is also nothing about turning off in site/game messages listed on the support page other then just deleting the messages yourself.

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