WI: Allies take Sokolniz Castle at Austerlitz?

What if the Allies were able to push the French out of Sokolniz Castle? Could they make an exploitable gap and push it to win the battle? Or was Napoleon's victory probably assured? If Napoleon lost how would that change history? Could the Allies turn the tides and beat Napoleon a decade early?
 
What if the Allies were able to push the French out of Sokolniz Castle? Could they make an exploitable gap and push it to win the battle? Or was Napoleon's victory probably assured? If Napoleon lost how would that change history? Could the Allies turn the tides and beat Napoleon a decade early?

Even if Nappy had lost Austerlitz I think he
was still too strong in 1805-6 ITTL too to
be finished(maybe if Prussia turned against
him then but I just feel Nappy would have
pulled another victory over them out of his
hat). Remember, IOTL it took a two-front &
Britain, Prussia, & Russia(aided by some
Swedish troops) to finally defeat Nappy in
1814-5.
 
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