There is such a thing as a B-corporation. https://en.wikipedia.org/wiki/Benefit_corporation

"A benefit corporation or B corporation is a corporate form in the United States designed for for-profit entities that want to consider society and the environment in addition to profit in their decision making process."

E.g., Patagonia is a B-corp.

"Maximize profit" is not a well-defined single thing. For instance, the suggestion that companies maximize profits without regard for their customers must explain why the customers actually stay with that company; in general that may be a short-term win but a huge long-term loss, and many companies have died that way. If nothing else you've got to consider long-term profit vs. short-term profit, and there are in fact many other "something elses" to consider (what level of risks to take, etc).

Maybe this is rhetorical, but there are a few that don't place "profit first". One such is http://en.wikipedia.org/wiki/Mondragon_Corporation

A "non"-profit? Different definition of profit, it's trying to maximize something else

Well the company I work for as one and any other company that realises the pursuit of money without regard for other ideals is an exercise in destruction and exploitation.

Often co-operatives will fit well in to this category as the workers in a co-operative are rather less likely to malevolently exploit themselves in a disdainful pursuit of profit before humanity.