The key mistake there is to confuse "focus" with "selling only one thing."
The fact of the matter is that the more focused your brand is, the more things you can actually sell.
This is because the narrower your focus, the more likely it is that you completely occupy a certain place in the customer's mind. Once you have "permission" to live there, you can become part of the customer's psychological life as well as their physical one, interrelate your functions with their other activities, and upsell from there.
In an ideal world, you start with a functional benefit offering - e.g. "Nike sneakers are better for running" - and then move on to an emotional one - "Nike = achievement." Soon everything stamped with the little Nike swoosh comes to mean "achievement," even if it's got nothing to do with the actions of the customer. Nike could sell business suits and they would make a bundle. Or even cars, maybe.
But you've got to understand your essence - the area the customer has given you permission to focus on.
Some other examples of brands that do this well: Google, Starbucks, McDonald's, Oprah, Microsoft, Conde Nast, The Kardashians, Tony Robbins, Harley-Davidson.
If you try to be "the everything brand" right from the beginning, ultimately you will go nowhere.
In the political realm, successful parties and leaders understand this principle. Not to leave anyone out, but two examples come immediately to mind: the Tea Party, which is associated with fiscal responsibility, and Michelle Obama, who is associated with nutrition.
Starbucks is losing its way because it has lost touch with that thing it owns in the customer's mind: a time-out with friends from hectic life. It isn't selling coffee or premium products at all. So in its quest for global expansion, the company is focusing on permission to sell ice cream rather than developing other experience-brands besides coffee shops.
If you own a business or are developing your personal brand, strive to do one thing better than anybody else, and then when you succeed, leverage that across expanded offerings.