I contacted EA support. I was walked through the following possible solutions:
1) Enabling in game overlay from Mass Effect 3 Origin games library.
No option available.
2) Enabling in game overlay from Origin website.
Again, no option available.
3) Uninstalling and reinstalling Origin.
Overlay prompt came up when Mass Effect 3 started, but when I attempted to launch multiplayer the game crashed. I tried this a second time with the same result. I was instructed to repair the game at this point. After the game repaired itself, the in game overlay no longer functioned, but the game no longer crashed when I started multiplayer.
4) Was asked to disable and enable the in game overlay again.
In game overlay still doesn't function
5) Log out of and shutdown Origin. Restart Origin, log back in, and start Mass Effect 3 again.
In game overlay still doesn't function
6) Agent consulted with "specialists". Was told that my "issue was registered with the experts" and they would be taking care of the issue for me. I just have to wait 24 hours and the problem will be fixed from my account.
Awaiting results. Will update next post with results.
Also experiencing this overlay problem with ME3 when trying to multiplay....
Hope EA fixes it soon with the holiday period nearby (july and aug).
But since i saw in this tread the issue was present since 2015 - i don't have a lot of hope for it ...
Was considering buying the origin vault to access more games - but find that they should fix their existing games first!!!
