what your talking about is same origin request that will not be possible without a backend which will make a cross site request to the project of your choice to process those requests, which will also mean allowing the backend basically admin privilege's which means you'll be trusting the user not to abuse it...
which may happen which is why i recommend against it, instead why not use level codes that are redeemable in other projects... just obfuscate it a little and boom perfect no need to overcomplicate something that may put your account into jeopardy just for that
also the use of a backend requires more than just CDO knowledge as well so just stick with the redeem codes or if you have a better idea than just implement that,
OR and this is very circumstantial is that you could combine a chatroom with a big project... much like featured [Battle Cars] did which actually could work considering if you don't have any assets to fork over for another project if you do this will take effort depending on animations and how much you have
as for your question of using other projects, i worked on an emulator which can run JSON but I'm not motivated enough to finish it since most of my questions got answered as i made it barebones runnable, but for now i'll end this tangent
TLDR: yes, if you have the knowledge to back it up and a lot of time to kink out bugs along with a major security risk for your account