One scenario that has been done to death on AH.com (though as far as I know never as a full-fledged timeline) is the British entering the war on the Confederate side (sometimes because of the Trent Affair, or a worse one) along with the French, and Russia and Prussia reacting by entering on the Union's side. The conclusion is always that the "CP" get curbstomped by the "Entente".
And then what?
For one thing, the CSA are now independent. But with what borders?
And what about Europe? There is certainly no War of 1870 and no German Reich.
I'm eager to read your ideas.