Menshevism was only a powerful force in the Caucasus, where it had been amalgamated with Nationalist forces. Otherwise, by the time of the October Revolution, the Mensheviks were in an alliance with the Socialist-Revolutionaries and left-leaning Kadets. The SRs didn't have a talented leadership or a solid ideology, but they were extremely popular and had the support of almost all of the peasants, so they went to the Mensheviks for an inspiring leadership and an expansive political platform. The Kadets went in on the alliance too, sealing the cracks with a little bit of their leadership and their rank-and-file.
So, how do you get these forces to take over Russia? You've gotta get rid of the Bolsheviks, somehow, the only ones who wanted to end the war as soon as possible, and who were willing to use violent means to an end. The Menshevik-SR-Kadet alliance, as huge as it was, was indecisive, and had there been no October Revolution, its probable Lenin would have led another putsch and another and another until he got his way.
Perhaps there is no October Revolution, or it fails, or whatever. The elections to the 1917 Constituent Assembly would have happened anyway, it was being planned and prepared for by the Provisional Government. Victor Chernov of the SRs becomes Chairman after an SR curbstomp. But he doesn't end the war soon enough. Come February, the Germans start marching through the Ukraine and the Baltics, sending soldiers retreating back into the Russian heartland to regroup with workers. Does Chernov surrender? If he doesn't, there will be another putsch initiated by Lenin, and this time it'll work. And the Mensheviks still haven't risen to power.
It just looks very difficult for the Mensheviks to take power. They weren't the type, and they weren't popular. You've got to go further back.