I am not aware of any extension to suggest that would do this. You would need to AJAX-ify the whole website/process.
Not sure why you would need to do this and what would be the advantages.
There could be some workarounds though, and here is a brief description of possible implementation. But keep in mind, that it might not be applicable or the right solution, as this depends on many things.
For example, you could create a small content plugin. Then in the same article you could write the content for the 2 languages, each one inside certain tags for being recognizable by your plugin, e.g.
{english}english text here...{/english}
{italian}italianos text here...{/italian}
You could instruct the plugin to wrap each language's content with a div that will have a special id.
Then you would also need to inject your checkboxes in each article page, and with some javascript you would be toggling the display of each language's div.
Furthermore, you could use a javascript cookie, to save user's selection for other articles.
Well, here are the downsides of the above suggestion:
You actually don't have a fully multilingual website, as :
- Metadata of the page will still be in one of the 2 languages.
- Both languages content will be in the same page.
- Modules and anything else system wise will still be under the main language.
- Not the best for SEO.
- Maybe not that easy to manage content for 2 different languages.
- and maybe more....
But the above solution could work in a scenario, where you simply want to present the same content to users in both languages with a button click, you don't care about SEO and any of the other downsides.
e.g. maybe you are creating a page where you want teach italians and want registered users to easily see text from english to italian and vice versa.
Ok... the above approach was a quick idea I had considering your question.