Lenin and the Bolsheviks did follow the general process Marx described, though. Can you elaborate on what you mean, here? Further, Marx used Socialism and Communism interchangeably, but referred to Communism in stages, such as Lower-Stage Communism and Upper-Stage Communism. Lenin simplified this to Socialism and Communism, and over time we have come to understand that we can go further and break these up into even more stages.

Marx wasn't around for the establishment of Socialism, his analysis was focused on Capitalism and how we may overcome it, not a prophetic view for how society must work. This isn't a knock on Marx, rather, by contextualizing his ideas we can avoid dogmatism.

As for cooperatives in a Capitalist system, no, not really. What you are describing is Utopianism, ie the idea that you can think of an ideal society and adopt it directly. The data surrounding cooperatives don't appear to indicate any danger to large firms and other Capitalist entities dominating markets.