How do I push all remote branches to a new/different remote?

I simply want to move an existing repository 'as is' from one place to
another (the another being github fwiw). I would like to keep all the
branch information intact.

That is,

git clone ...existing remote repo...
cd ..
git remote add ...new remote repo..
git push ...you tell me..

So, there are *no* local branches to bother about, but I have hundreds
of remote ones. I can't spot a way to do this.