Diseconomies of scale refer to a business that have grown too large for their given market. This means that rather than experiencing continued decreasing costs per increase in output, firms see an increase in marginal cost when output is increased. Basically, the more is made, the higher the production cost. This can happen for numerous reasons, but all of them come back to the company being too large to function efficiently.
A perfect example of this is the car company General Motors (GM). Over the years, GM has grown so large and has so many branches that it is just as likely to steal customers from itself (GMC vs Chevrolet) as it is from other companies (GMC vs Toyota). This ends up costing GM a fortune in time, money, and resources, and the company has become a diseconomy of scale.

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here is another video in which a guy tries to visit, make a purchase, and consume a good at every Starbucks in Manhattan. He discovers that this is a nearly impossible task, as there are one hundred and seventy one Starbucks in Manhattan alone (just one borough of one city in one state)!

http://financial-dictionary.thefreedictionary.com/Diseconomies of Scale

Is it possible for a firm to grow too large? If so, what is it called?

answer: yes, a diseconomy of scale