I create my own T-shirts and then publish them on teepublic.com They do not have a color limit, although I am have done color limit t-shirts before with great success. These designs used either Adobe Illustrator or Photoshop.
Pokemon inspired vector art. One for each Pokemon Go team. I used the colors of the shirts to incorporate into my design, leaving no lines and letting the eye complete the picture. Illustrator.
A fun to design fake ugly Christmas sweater; Overwatch style. Simple, one color, and evokes the patterns of the Overwatch characters I chose to represent and Christmas icons. Illustrator.
Another Overwatch inspired design. The character's name is Junkrat, so I turned him into a literal rat. Photoshop.
While not pictured on a t-shirt, this was a special one-time design for me and my boyfriend. On the left is my dog Jude, and on the right his original character, also named Jude. Photoshop.