Russian Revolution WI: April 20th (May 3rd) 1917: Provisional Government collectively resigns.

As it says on the tin:
On May 3rd (old calendar: April 20th), the Contact Comission between Prince Lvov's Provisional Government and the Ispolkom meets. The Ispolkom demands, once again, the unambiguous clarification of the Provisional Government that they pursue a peace "without annexations or indemnities" and do not pursue Russian control over the Bosphorus.
IOTL, the Provisional Government rejects communicating such a message to the Western Allies for fear that the latter would stop their financial aids to the near-bankrupt Russian government if Russia's continued war effort was thrown into doubt, and perhaps condone Japanese meddling and occupations in Russia's Fear East under such circumstances.
The cabinet threatened the Ispolkom with a collective resignation, should Ispolkom insist on its demand.
IOTL, Ispolkom cowed and acquiesced with the mere resignation of Foreign Secretary Milyukov, who was made into the scapegoat of the affair.

But what if Ispolkom had remained tough - and what if (because that of course does not strictly follow from the first) the Provisional Government really steps back collectively? on April 20th / May 3rd 1917?
 
Does someone in the leadership o the soviet movement who can build coalitions (i.e. not Lenin) find their balls to go for full (temporary) soviet power? Does Stavka try military dictatorship? Is Kerensky grabbing what he can? Anarchists and Bolsheviks up to no good? Someone trying to include armchair politicians from the Duma? Or all of the above?
 
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