The cascaded connection of power converters extends conversion ranges but requires careful consideration due to high component count and efficiency concerns, as power is processed redundantly. Furthermore, using several active switches that must be turned on simultaneously may introduce significant drive and control complexity. To overcome this limitation, single-switch quadratic DC-DC converters have been proposed in the literature as a prominent choice for various applications, such as light-emitting diode (LED) drivers. Nevertheless, the motivation behind the conception of such topologies, beyond extending the conversion ratio, remains unclear. Another unexplored issue is the possibility of obtaining single-switch versions of cascaded converters consisting of multiple stages. In this context, this work investigates the synthesis of single-switch non-isolated DC-DC converters for achieving high step-down and/or high step-up based on the graft scheme. Key issues such as the voltage gain, additional stresses on the active switches, component count, and behavior of the input current and output stage current are addressed in detail. An in-depth discussion is presented to identify potential advantages and shortcomings of the resulting structures.