For decades, the design of reflectarray antennas followed a unified strategy of selecting a certain unit cell for the whole design. After that, the dimensions or orientations of this unit cell are changed to achieve the required phase shift at each position on the reflectarray surface. This strategy requires a 360° span of the phase characteristics of the selected unit cell versus a control parameter. In addition, it requires maximal linearity of the phase characteristics of the unit cell. This paper considers a different and more flexible strategy for the design of reflectarrays. This strategy is based on switching between unit cells to make use of the regions of the characteristic phase curves of best linearity for each unit cell. With this strategy, we can use unit cells with similar polarization, and unit cells that do not span 360° in phase characteristics in the design process of the same reflectarray. The single criterion for switching between unit cells is the maximal linearity of the phase characteristics of the unit cell at the required phase. This strategy guarantees maximization of the gain, and minimization of the side-lobe level (SLL) at the design frequency. The proposed strategy is validated for the design of a reflectarray antenna to work at 28 GHz using five different unit cells for possible 5G applications. The simulation results reveal the feasibility of the proposed strategy for achieving high gain and low SLL at 28 GHz.