Still failing to add additional checkout SSH keys

I am 100% sure this is possible. It was discussed recently here:

Would you create a minimal working example that people can look at? I suggest you make a single public GitHub repo, and show all the steps you have taken to checkout a secondary repo.

(You may find that someone will clone your repo and amend it to do the secondary clone on one of their own private projects, but they might not go to the trouble of constructing all of that from scratch).