AHC: Have two European Powers intervene on opposite sides of the ACW

What series of events might lead two or possible more European powers to intervene in the ACW and turn it into a more global conflict? Any powers would do, and any point of divergence will do. Is it even feasible?
 
Britain and France join the Confederacy (this is pretty ASB).

Bismarck seizes the opportunity and attacks France while the majority of its professionel soldiers is bound in north America.

Italy tries to conquer the Papal States (war with France), while Austria, fearing German and Italian nationalism joins France and declares war on Prussia and Italy.

Lincoln, fearing to loose the war due to Austrian, French and British superiority begs the Russians to join the war.

The Czar sends his units into Austria and some to the American west coast.

The Ottoman seize the opportunity to get his old lands back and attacks Russia.

So you have:

The Confederacy, allied with
- Britain
- France
- Papal States
- Austria
- Ottoman Empire

The Union, allied with
- Prussia
- Italy
- Russia
 
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