The ability to consider a wide range of solutions to a design problem is a crucial skill for designers, and is a major differentiator between experts and novices. One reason for this is that novices are unaware of the full extent of the design space in which solutions are situated. To support novice designers with design space exploration, we introduce Mixplorer, a system that allows designers to take an initial design and mix it with other designs. Mixplorer differs from existing tools by supporting the exploration of ill-defined design spaces through "social design space exploration." To evaluate Mixplorer, we conducted (1) an interview study with design instructors who reported that Mixplorer would ``help to open the minds'' of novice designers and (2) a controlled experiment with novices, finding that the design-mixing functionality of Mixplorer provided significantly better support for creativity, and that participants who mixed designs produced more novel designs.