The White Army lost the Russian Civil War due to ideological differences, poor organization, and lack of supplies. What would have helped their efforts?
I would assume that if Constantinople had fallen during WWI and opened the Bosporus to the French and British, perhaps Denikin could have gotten more supplies to fight the Communists with.
As for ideology, some officers were monarchists -- Kolchak and Wrangel, most prominently. Others, like Denikin, Kornilov, and Yudenich, supported a Western-style republic. Would there have been a way to compromise?
I question the idea of the return of the czar*. The reintroduction of that office would at least appease the royalists to some extent, but then there's the question of the Russian people. After Nicholas II, Alexandra, and Rasputin, the crown would leave a sour taste in their mouths.
That would be the reason for the Duma and Prime Minister to have the most say about the state. If they have a czar again, it seems that it would need to be a British-style system where he has no say in politics.
Just a thought.
*It would be too late to save Nicholas and his family at this point, as the Ekaterinburg execution had already occurred.