Something I find fun and palette cleansing in between bigger projects is taking an existing company logo and creating a design around it. These aren't necessary meant to be anything more than an exercise, but sometimes they can be a good way to show your interest in working with a certain company or getting their attention. Doesn't always do the trick but it can get your work out there and show off your creative side.
I tend to stick with companies in the area that I focus on for my main work, mainly gaming, so those are the logos that I play with. This isn't to say you need to stick to a niche - there are plenty of big brand logos that you can have a crack at. Main thing for me is to have fun with them and let your creativity drive the design - it's a great way to loosen up and get your brain thinking of different ways to incorporate this odd shape into your work.