I think the sentence is referring to 'social classes' as in the working class, aristocrats etc. The social order in society essentially. I think the sentence means adapt to largest group, or party, so that they can live with people of different walks of life. Could I have the context please because at the moment the sentence seems a bit odd? Hope i could help:)

It is referring to the different social classes which exist in society. The 'masses' are the majority of people who we tend to refer to as either 'working class' or 'middle class', depending on their social backgrounds and opportunities.

"The classes" means "the upper classes." Sometimes "classes" can mean that. The adjective "classy" can mean high-end or luxurious. The phrase you've quoted sounds outdated to me, though. It sounds like something from the 1940s. In 2015, in the United States, we rarely use the phrase "the masses." The phrase means in order to get rich ("live with the classes") you should market to "the masses." This would fit quite well into an imaginary dialog between a film critic and a 1940s Hollywood movie mogul. Critic: "Why don't you make better, more artistic movies?" Mogul: "Artistic movies don't do well at the box office--they don't make much money. Cater to the masses to live with the classes."