Ehm, Pocus, this is AACW, not NCP. We can promote 3*** to 4**** there, can't we?
AFAIK, U.S. Grant even gets his "strategist"-trait only when being promoted to 4****. Or at least he did the last time I promoted him, in 1.07e or f...
So, yes, it is possible to promote a general to 4****, it even can make a difference, but the only thing that helps pushing it is having the 3*** in question win battles, battles, battles...

Remember, historically it took U.S. Grant nearly 3 years to be promoted to Commander-in-Chief (until March 1864), in the game he usually won't need quite that long but it can take more than a year or two as well...
Regards, Henry

Henry D, also known as "Stauffenberg" @ Strategycon Interactive and formerly (un)known as "whatasillyname" @ Paradox Forums
"Rackers, wollt Ihr ewig leben?" (Rascals, Do You want to live forever?) - Frederick the Great, cursing at his fleeing Grenadiers at the battle of Kunersdorf
"Nee, Fritze, aber für fuffzehn Pfennije is' heute jenuch!" (No, Freddy, but for 15p let's call it a day!) - Retort of one passing Grenadier to the above
