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Your challenge, if you choose to accept it ;), is to have the 2nd Mexican Empire survive and to wank it as much as possible. Have fun!

EDIT:
Okay then by popular demand I will provide this setup:

From Johnrankins Victorious CSA in turmoil
May 1864 Hood doesn't back-stab Johnston and attacks as ordered. Sherman forced back.
Sept 1864 Sherman finally reaches Atlanta as he had to take much more time getting there than OTL.
Nov 1864 Little Mac elected Sherman takes Atlanta 3 days after election
Feb 1865 Little Mac sworn in
Apr 1865 Due to presidential interference the Union Army is being forced back
June 1865 President McClellan assassinated President Pendleton assumes office
July 1865 Cease-fire with CSA negotiations begin
Jan 1866 Peace treaty signed
The CSA is made up of Texas, Louisiana, Mississippi, Alabama, Georgia, Florida, SC, NC and Va south of Rappahannock and WV remains a Union state. Free trade with the US.
Inflation rate down to 400% a year

Now according to Wikipedia
Fearing the French would continue their campaign to El Paso del Norte, President Juárez relocated to El Carrizal, a secluded place in the mountains near El Paso del Norte, in August 1865, . It would have been easy for the French forces to continue in pursuit of President Juárez across the border, but they feared altercations with American forces. General François Achille Bazaine ordered the French troops to retreat back to the state of Durango after only reaching a point one days travel north of Chihuahua City.
In TTL with the ACW still raging the French forces do not hold back due to the fear of altercations with the Americans (US or CS). The reach El Paso del Norte and track Juarez's men. Then begins the battle of El Carrizal that ends in Juarez's capture.

With this occuring before Maximillian's 'Black Decree' of OTL Juarez, and select Republican leaders including Porforio Diaz, and left alive so as to not lionize the populace loyal to them or to alienate moderates. Instead they are instead exiled to the Islas Marías.

After this Maximillian continues, as in OTL, to panders to the indigenous peoples. He did this OTL, and it worked like a charm on winning over the indigenous population in the south.

Empress Carlota began holding parties for the wealthy Mexicans to raise money for poor houses. One of Maximilian's first acts as Emperor was to restrict working hours and abolish child labour. He cancelled all debts for peasants over 10 pesos, restored communal property and forbade all forms of corporal punishment. He also broke the monopoly of the Hacienda stores and decreed that henceforth peons could no longer be bought and sold for the price of their debt.
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