This article presents a thorough study of spherical probe-corrected phaseless near-field measurements with the two-scans technique. Such technique is based on retrieving the antenna under test radiation pattern from the measurement of the near-field amplitude signals on two spheres of different radii. The postprocessing of this type of measurements results in a highly nonlinear algorithm, prone to get trapped in local minima and provide incorrect solutions when the measurement conditions are not properly selected. Through a series of numerical simulations, the influence of different measurement parameters on the phaseless technique is analyzed. It will be shown how both the relative and absolute values of the measurement spheres highly affect the convergence of the phase retrieval algorithm. The type of AUT and its radiation pattern characteristic also play a fundamental role in the feasibility of phaseless measurements. Other parameters such as sampling rate, noise, probe correction, polar truncation, and measurement offsets are also investigated. The conducted study allows to extract a set of guidelines to improve the accuracy of phaseless spherical near-field algorithms. In addition, purely phaseless antenna measurement examples are given to demonstrate the algorithm capabilities and limitations, and to validate the developed numerical investigations.