“Would you consider going into business with me?”

You're going to start a gourmet catering business. You want your friend to join you as a business partner. You told her about the kind of business you want to start, and she seemed interested in it. You ask her:

Would you consider going into business with me?

would you consider (doing something)

You ask "would you consider ___ing" when you want to carefully and politely propose an idea to someone. You usually use this phrase when asking about big and important decisions. For example:

Would you consider moving in with me?

Would you consider coming over to work for us?

go into business with (someone)

To "go into business with" someone means to start a new business with them or to join them as a partner in the business. A "partner" is usually someone who gets a % of the business, not just a salary.