What were some of the philosopies that appeared as a result of the success of big business during the Industrial Supremacy?
Although laissez faire capitalism and Social Darwinism were two important philosophies of this time, there were at least two others that need to be mentioned in a good answer to this question.
First, you have the idea of the Social Gospel. This was the idea that Christians needed to be more socially conscious. It said that they needed to do something to help all the people who were being hurt by the rise of industrialization. This helped lead to many Progressive efforts such as settlement houses and some labor laws.
Second, there was the Gospel of Wealth as espoused by Carnegie and others. This was the idea that the rich had a responsibility to help others. However, it held that the rich were also better than everyone else and should therefore act paternalistically. In other words, the rich should use their money to help others, but they should not give their money to others. They were better than everyone else so they should be the ones to say how the money would be used.
I think that you can find many of the philosophies that appeared during the rise of Industrialization would be ones that enhanced the role of business and commerce in social orders. Naturally, Adam Smith's development of the free market and the notion of self interest was one philosophy that helped set the capitalist ball rolling. Smith's assertion in the overall just nature of the marketplace and the idea that external regulation was not needed as a direct end helped to really bolster the pursuit of self interest and economic growth. Another philosophy that helped to emerge in the assisting of business growth was the idea of Social Darwinism. This misapplication of Darwin argued that natural law justified a "survival of the fittest" reality. In this light, essentially, anything goes. This philosophy was used as a rationale for business interests to override all other concerns and one another as profit was equated with survival.
In Who Owns America? edited by Agar and Tate, the article by Tate, and one other by Douglas Jerrold, will give you a real good introduction to one philosophy that appeared as a result of the success of big business. I have been told that I'll Take My Stand by Twelve Southerners is a better exposition of this philosophy, but I have never read it.
There is a scholarly review of Who Owns America? at jstor.org; your library probably has a subscription to this data base.