To build on Phil's great start, here is how I think it should work.

Question is Asked

A user on physics asks:

How Do Bicycle Spokes Work?

This is assigned a post ID of #94,0001 on physics. It is a physics question.

Cross-site Users Show Interest

hippietrail with accounts on both sites is browsing physics and sees this question and thinks it would be great on bicycles too. So he clicks a button:

Recommend on Other Site

This brings up a list of the sites he is a member on and allows him to pick which one wants to suggest it as a good fit for. Other users can see this on the question as they would a close vote:

They can either up-vote or down-vote the cross-site recommendation perhaps along the lines of a review or somesuch.

^{Both suggesting cross-site posting and voting on existing suggestions should be only visible/available to high-rep users on the destination site}

Review Gets Created

On both the target-site and the original-site a review task for trusted users gets created. For the original-site they are allowed to vote either:

Migrate or Cross-Post

For the destination-site they are allowed to vote either:

Accept or Reject

If the receiving-site votes 'Reject' it does not get sent regardless (it stays on the original site akin to a rejected migration). If the receiving-site votes 'Accept' then it gets Migrated or Cross-posted depending on the choice of the original-site voters.

Managing Post IDs

We know how migrations work, so let's ignore those for now. The original-question has an ID of #94,001 on Physics, and it and any answers get new IDs on Bicycles. Post-type in data.se could be set as 9 - Cross-post to be able to distinguish the origin of each post since it is existing in two time-stack continua at once.

^{Yes, continua is the plural of continuum apparently. Latin, it's dead for a reason folks.}

Any additional answers tacked on would be automatically assigned an ID on any shared site(s) with the same cross-post PostTypeID while being assigned a proper answer ID on the site it originated from.

Voting on Cross-Posts

If you are on Physics when you vote:

1. Votes/flags on Physics-originated posts are treated as normal
2. Votes/flags on non-Physics posts have no impact on reputation/score, but impact display

If an answer accumulated too many downvotes/flags that originated on a different site, it will be hidden from people accessing the question from the physics side. The answer may be good for bicycles, but not have so much benefit to the physics readers. And that's fine. The same would happen the other way around too. So we hide any inappropriate answers that a site's community deems aren't right for them (but don't lose them from the other site).

Hiding Cross-Posts from New/Google Users

For new users (under the association bonus level) and for google crawlers, only answers originating from the site being browsed should be applied. This means that bicycles.se answers will be more bicycle-oriented for search terms, and physics.se answers will focus more on the physics and differentiate the search results (hopefully). New users will not be confused by the potential for very contrasting answers or other issues related to differing community standards without losing out on anything.

Moderating These Questions

Locks/Protects would be per site and not mirrored on the other site (no sense in preventing good answers to be given on Physics for issues with the popularity on Bicycles).

Close votes would work as follows:

• Closed on original site ▶ Migrated to target-site
• Closed on target-site ▶ Treat as rejected migration

Flags on questions by users of either site would only be shown to trusted users/moderators of that site (no moderation of the other communities' questions).

I think this is a tremendous idea and will reduce poor migrations as well as give people a much better resource for comprehensive information on a cross-discipline topic, improving the quality of SE as a resource.

I imagine this might be better if, instead of multi-posting the same question on multiple sites, allowing the same question to be shown on multiple sites, and show up in the search results for those sites, while remaining just one question in the database.

I understand that this would come with some challenges, such as determining which tags should and should not be used (per-site), but it would be a cool way to see how different communities can contribute to the same question.

Answers could then include an icon indicating which site the user answered from, and badges or reputation would be only for that site, simplifying this. Furthermore, it gives users of one site an idea of what the other communities are like, and may get more users on the sister sites.

This approach could also work either by letting the OP specify which sites to share on (and those sites can close it on their respective sites), or this could be something left to reviewers with high enough reputation - but either way I think both models would work.

I would support such a feature.

I feel the segmentation of SE sites has become a bit excessive (e.g. SO, Code Review, Programmers and CS). This causes the average user (like myself) to worry more about where to post than how post correctly (partially because of fear of being scolded by the more hard-core users). In my case it ends up with me completely giving up on the post and searching for answers elsewhere.
I think that cross posting would allow the average user to post the question in the most fitting site (without worrying about not reaching some potentially interested experts), and use the cross-post feature to try suggest that the question be published on another site where the question might also be relevant.

I do agree with some other answers here, that in some cases, a question that fits more than one SE site might be indicative of a bad question, but I believe that these cases are not the majority. In any case, I don't think that such feature, if moderated correctly, would contribute to more bad questions being posted.

I like this idea, and agree with the rationale insofar as it helps a question reach an interested audience (not creating clutter, iow).

Some potential challenges:

• User privileges -- ability to edit, delete, etc. -- greater on the shared-with site than the originator site... Is that OK?
• Tags -- how would those be treated?

Implementation ideas:

• add this as a review category (?) -- for reviewers to include/exclude questions nominated for sharing?
• add a new privilege category (?) -- so a person who wants to nomiate a question to be shared with SO, for example, would have to have some level of rep on SO?

--EDIT--

Re-reading this post / some of the answers that have come-in later...

One perspective that I think hasn't received much attention here is the cross-suitability of the answer to the cross-posted question. It's one thing for a question to be relevant to two sites (using the 'how bicycle spokes work' example on @jmac's great answer here); but it may be quite another thing for the answer to be relevant on both sites. For example, I can imagine readers on the physics SE will be more interested in answers describing the different types for force and how they be modeled using physics formulas, etc.; and I can imagine the readers on the bicycle enthusiasts' SE site being interested in an entirely different sort of answer (maybe something more focused on performance comparisons with alternative wheel designs on/off road, etc.).

I don't have any great ideas for where to go with this, but it seems like something that should be part of the discussion / proposed solutions.

I don't think there should be any crossover feature that would allow posting a single question on multiple sites (how should edit/close priviledges be calculated for the users of both sites?). The sites should be designed so that the topic crossover should be an exception, not the rule.

However, there are many common interest areas, so I'd vote for the idea of stronger linking between sites. For example, by adding a network-wide linked and related questions section on the left side. The question would always belong to one site, but it would be easier to browse related questions on the other sites.

For example it could look like that:

Linked (Travel)

• question 1
• question 2
• question 3

Linked (other SEs)

• question 4 (The Great Outdoors)
• question 5 (Physical Fitness)
• question 6 (Photography)

Related section would be more tricky to implement, because network-wide looking for duplicates must be something more intelligent than simply word-based (I don't think people on Pets would be happy seeing Python programming questions in every second raptiliae question).

This has been roughly implemented on the international sites for the use case of linking from Stack Overflow in English to canonical questions written in other languages.

If you go to certain questions on Stack Overflow and your browser language is set to one of the non-English languages that we support, you might see a small banner letting you know that we have a nearly identical question on [language] site, with answers of comparable quality. This works by users on the international sites nominating pairs of links (originating from English site, landing on international sites) which are vetted and put in place.

All of this currently runs on stuff that isn't quite in the code base properly, and probably won't be until Channels is quite a bit more feature complete. But, some functionality does exist.

I'd personally like to have something similar to what has been proposed in various forms here eventually; it would be great to lessen the fragmentation between SO and sites like Software Engineering, for instance. However, I can't give a definitive timeline on an implementation, or what that might eventually look like.

I'm tagging this as deferred as it is something that I really want to explore, but I can't give any promises on when we'll be able to do it. I can say that getting the rough implementation that we have going for the international sites more 'properized' and supported with UI that doesn't require user scripts is a big priority for me once resources become available, so the idea as a whole is definitely near the top of the list of stuff I want to see get more attention as soon as we're able to provide it.

Cross-site question association

I suggest to extend question association mechanism to all StackExchange sites. It's already working between mechanism between StackOveflow in Russian and StackOverlow in English.

Something like this

_{Text translation: This question has answers on StackOverflow in Russian. [link to associated question].}

If very similar questions were asked on different StackExchange sites (that have some topic intersection) we can show link under associated questions This question has answers on [StackExchange site of associated question]. [link to associated question]..

I totally agree that as the number exchanges/communities have grown, a lot of overlapping questions are spreading across the lines between the communities.

I also agree Migrating a question that was posted in the "incorrect" Community is not really a good fit for these questions.

1. The OP participates in and posted in the original Community because he thinks that is where it belongs. He has already expressed what he thinks the "correct" Community it.
2. Once the question is migrated (if that is possible), content that was posted in the originating community is often lost.
3. Often the decision of which Community is the one-and-only-one "correct" Community is highly subjective, a situation Stack Exchange generally tries to avoid.

I had noticed this and recently proposed a different way to addressing the problem - Let Communities refer questions to other communities.

I do like your solution as well; but, as a developer, it seems that it might be more complicated to implement. I believe a lot of the problem could be addressed by allowing visibility of the referred questions to other Communities but still allowing them to remain in the original community.

You have some great points, however the reason it will not currently work is because of the point systems being individual to each site.

And the badges primarily being individual to each site.

I could see improved performance on users using multiple sites if there were more badges added to stack overflow that were based on the point/reputation of other sites.

I don't necessarily think it would be good to add a whole lot more badges, to the already numerous gold/silver/bronze badges there are. What I think would work, is to create a platinum badge or something, that is relative to how many sites you have a total rep score of over 1000 points or something.

I suggest that there be a Network tab, or similar options to display interesting questions from across the network.
Clicking on questions from this tab would take you to the orignal question on it's "Real" site.

This suggestion is otherwise very similar to https://meta.stackexchange.com/a/219824/144630

I suggest the list of questions to be shown on that list be manually curated. With the curation being an unlockable privilege determined by reputation on both sites.

Possibly with:

• "Add to cross-site list for X", requiring some level of rep on both sites. Probably 100 would be good, since the assoication bonus kinda indicates "You get Stack Exchange enough to have some respect everywhere in the network".
• Removing being similar to close-voting, requiring 4 votes by people with a certain privilege on the receiving site (probably lower than close voting).

Mock-up:

Yes the mockup image is inconstant, in formatting, but it is just example.

I'm not entirely happy with the idea of it as a Tab, but I think it does benefit somewhat from being on a separate list to the real questions on the site. So users who just don't care can ignore it. (I would expect a lot more cross-posts than migrations, so leaving it in the main lists might not be good. Or it might be Ok)

I came across this question in during the process of writing a related question: Multi-Topic / Cross-Topic Question: Search Visibili...

This question is also very similar to 2012-META: Asking on Multiple Sites: “Soft-Migration”.

I'm wondering if a simple patch solution could be to fill out search results with Q&A from related topics/sites? I think this would help improve question visibility and also help provide more answering opportunities to casual users around StackExchange.

Take my example:

• diy_search=affinity+fan

• engineering_search=affinity+fan

As of April 2019 there are only ~4 search results total across both topics. wouldn't it make sense to supplement searches like this with possibly relevant material from related topics? Possible results could be limited to only questions with relevant tags, residing in specified coordinating topics...

It looks like some related work has been done on this within the past 2 years for foreign language topics/sites, as detailed in Vadim's answer, although I'm not sure exactly how it works, and if it is applicable more generally. Does it just put a note on the question itself? What if I don't open the question? what about question browsing?

I'd like to suggest modifying search results. Perhaps only for searches with fewer than 10 hits?

Also, side note, perhaps the association bonus could be replaced by bonus-points and badges existing between specific coordinating topics on a per-topic basis.