Analysts of specific application domains, such as experts in systems biology or social scientists, are often interested to visually analyze a number of different network structures in conjunction, for example by using various visual structures of so-called multilayer networks. From the perspective of the human analyst, a sufficient perception and, consequently, a good understanding of those visual representations of multilayer networks is a non-trivial and often challenging task. Despite this practical importance and the clearly interesting visualization challenges, only few evaluation studies exist that investigate usability and cognitive issues of complex networks or, more specifically, multilayer networks. In this position paper, we address two main goals. On the one hand, we discuss existing studies from the fields of human-computer interaction and cognitive psychology that could inform the designers of multilayer network visualization in the future. On the other hand, we formulate first tentative recommendations for the design of multilayer networks, identify open issues in this context, and clarify possible future directions of research.