Alright so what if Kerensky accepts Kornilovs demand and a directory is formed. The directory consist of Kornilov(military) Kerensky(SocDem) Savinkov(NatSoc) and also Julius Martov(Menshevik). There is no defense of Petrograd, because Kornilov got his way and now has no reason to march on Petrograd. And the Petrograd Soviet won’t launch there own coup because they also have representation. Most importantly Bolshevik support and influence is diminished. Would this be a government that satisfies all?
Martov is never going to go along with this.
"...In June 1917 Martov professed his alarm that the Provisional Government might summon 'its praetorian guard from the front [and] play the role of a Cavaignac'. This, he conceded, would have the beneficial practical effect of eliminating the Bolsheviks as a political force in Russia. But it would also destroy the Soviets, and in particular the Petrograd Soviet—-to which Martov, not coincidentally, was addressing when he evoked the precedent of Cavaignac's betrayal, of which he knew everyone in his audience would be cognizant.
"After Martov finished, Iraldi Tsereteli assured him that neither he nor the Mensheviks nor the Russian proletariat had anything to worry about. Martov's analogy, he explained, was mistaken:
"'Comparing our revolutionary army with the soldiers of Cavaignac, you forget that the nineteenth-century revolutionary stereotype is quite inapplicable to our revolution. Then the bourgeoisie, relying on a conservative peasantry and an army composed of such peasants, disposed of the proletariat and paved the way for the victorious counter-revolution. But the army of revolutionary Russia is part of the revolutionary peasantry, and is at one with the working class in the soviet ...in consolidating liberty.'
"Tsereteli may well have been correct in dismissing the chance of a Russian Cavaignac marching on Petrograd, disbanding the Petrograd Soviet and the Provisional Government. and instituting a military dictatorship. That Kornilov, who was the closest (albeit still distant) equivalent of both Cavaignac and Napoleon Bonaparte in Russia in 1917, was unable to do this—if that in fact was his actual intention—suggests that he was. But the Georgian Menshevik, who had no illusions about Lenin's benevolence (or about Stalin's), fell prey to a different delusion when considering the Mensheviks' options should a genuine Russian Cavaignac appear. In that instance, he assured the Bolsheviks, 'we shall fight in the same ranks with you'.47 Such a scenario, one can suggest with some confidence, would have been an excellent example of the cure being worse than the disease..." https://books.google.com/books?id=5UKjDwAAQBAJ&pg=PA369
Indeed, by July Martov had already called for a government excluding the "organized bourgeoisie":
"The offensive had collapsed, and the first coalition government with it. With the resignation of the Cadet ministers on 2 July, Russia faced another political crisis. The workers and soldiers of Petrograd and Kronstadt grew more and more restless and hostile to the government and to the leaders of the Soviets who supported it. The 'July days' were at hand. Whether tinder the pressure of these events or as the result of his own belated realization that, 'bourgeois' or not, his revolution was in danger, Martov came out on the morning of 3 July with a demand for a new 'democratic' government based largely on the parties represented in the Soviets, without the organized bourgeoisie.' He admitted that up to this point he had regarded the passing of power into the hands of the Soviets as undesirable, but had changed when the resignation of the Cadet ministers showed that the entire organized bourgeoisie was relinquishing power. Such bourgeois ministers as stayed on, e.g. M. I. Tercshchenko, I. V. Godnev, or N. V. Nekrasov, represented no one but themselves; no reason remained why 'our ministers ought to remain in a minority in a coalition govemment.' 'History demands,' Martov declared, 'that we take power into our hands'; at least a majority of the Provisional Government ought to be made up from the Soviets, for there was no doubt that if the whole of Russia were asked, 'the revolutionary democracy would support us'. The main tasks of that new 'democratic' government, as he saw them, were to carry Russia through to the Constituent Assembly and above all to 'tear Russia out of the embraces of the war which strangles the revolution and prevents the consolidation of the conquests of the revolution'.. Its practical programme should contain the following points:
"(i) immediate peace negotiations with all sides renouncing annexations and contributions, and recognizing the right of nations to self-determination; Russia to withdraw from the 'imperialist war' and democratize its army for the purpose of defence against 'imperialist designs' from whatever quarter;
"(ii) thorough reorganization of the bureaucracy by means of a purge of all its counter-revolutionary elements;
"(iii) preparation of measures to enable the Constituent Assembly to realize within the shortest possible time an agrarian reform on the basis of the confiscation and handing over to the people of all land belonging to the Crown, monasteries and landowners..."
https://books.google.com/books?id=K663PZgP3s0C&pg=PA155#
You get the idea. Martov (like his counterpart in the SR's the center-left SR Chernov) was the sort of person Kornilov wanted shot--to him, such people were hardly distinguishable from the Bolsheviks.