Ok - so the saying has been used a bit too much. But it still works. Thinking outside the box means putting things in a different context. As an example, sometimes ordinary sayings can become catchy slogans if put in a new context or expressed in a new way.
Nike's slogan, "Just do it" is a classic example. (An imperative slogan - see types of slogans). They didn't create the slogan, it was a common saying. Many moms and many bosses had been saying it for years. But Nike put it in a new context. What they are saying is that most sports aren't complicated and don't require a lot of special equipment, just a comfortable pair of shoes and a ball. The key thing isn't the equipment, it's doing it.
Applying a slogan that already had a meaning to people made the slogan catchy. It sticks.
Other ways to get slogan ideas.
Mind Mapping Over Lunch
Buy everyone pizza and have them meet in the lunch room. Set up three flip charts and bring some markers. If the slogan is about a product, put a picture of the product somewhere. If the slogan is about a service or a part of the company, use something that represents it and attach it to a wall. Ask the group what words they use to describe the product. Write these on one of the pads. Ask them to use verbs that describe how they use the product. Write these words down on another pad. Then ask them what the product is like or similar to. Write down these words on another sheet. Then start to randomly match the three lists of words. A slogan often emerges immediately but if not, this should give you some ideas that you can go back to your office and work with. It's not exactly a mind map but it is a similar type of brainstorming that usually arrives at a result.
White Board Graffiti
This technique similar to the one above but modified so it can be done over a longer period of time in circumstances where it is difficult to get everyone together at the same time. Put a white board in the lunch room, waiting room or similar place and invite people to say what they think or draw pictures to express what they think of the product (or whatever it is). Perhaps provide an incentive such as a gift certificate for the most expressions of ideas. From time to time, go in and take a picture of the board. This may give you the words you need to write some slogans. If not the specific words, it will give you an idea of what people are thinking and how they will respond to your words.
Record Some Stories
Get some people together in an informal setting, provide some refreshments and get them to tell some stories related to their experiences with the product. You need their permission to have a recorder running, but they will soon forget that it is there. Chances are, they will have some stories that do one better than the last. If this kind of dynamic is encouraged, you will likely get some spontaneous expressions that can be modified into the slogan you need.
Sometimes creative people will beat their head against the wall to get ideas. Remember that the people you work with and the customers in your store or waiting room are a resource that you can draw on for the expressions you need to tell your story in a few words.