I've a suggestion that I think would be great and save some time. Let's say I'm browsing the tag "c++" in GameDev looking for a specific question, I can't find it in GameDev so I decide to check it in Stack Overflow.
Normally I'd go to stackoverflow.com and click [c++] again, however, wouldn't it be easier if in GameDev there was a button saying "See this tag in other Stack Exchange sites" and you could quickly search for the same tag in Stack Overflow, Programmers or other site?
Major problem with this: there's no telling if the tag with that name even means the same thing on another site. All the system can really do is search all the other sites and say "a tag with this name exists on these sites too." But that doesn't really mean anything at all when you come across tags like "email" and "united-states". We're then in the ballpark of displaying useless information that will only serve to confuse the users seeing it.
Your best solution: add a link to the other site in the tag wiki, if it's really that important. That way there's a human definitively saying "this tag on this other site is related to our tag on our site" and we're not just linking to random tags on random sites that may not be relevant to the user whatsoever.
You can also create new Question Filter in your Stack Exchange account.
For example I've just created a filter that take questions tagged c++ from both Stack Overflow and Game Dev sites: https://stackexchange.com/filters/71488/c-on-stack-overflow-and-game-dev
Only downside of this is that it can give up to 100 latest questions.
