Recent measurements reveal the presence of several features in the cosmic-ray (CR) spectrum. In particular, the proton and helium spectra exhibit a spectral hardening at $ GV $ and a spectral steepening at $ TV $, followed by the well-known knee-like feature at $ PV $. The spectra of heavier nuclei also harden at $ GV $, while no claim can be currently made about the presence of the $ TV $ softening, due to low statistics. In addition, the B/C ratio also exhibits a hardening at $ GeV/n $ and seems to be rather shallow at $ TeV/n We propose a possible explanation of the observed spectral features in the framework of a composite diffusion scenario and considering different classes of sources. The proposed scenario is based on two assumptions. First, in the Galactic disk, where magnetic field lines are mainly oriented along the Galactic plane, particle scattering is assumed to be very inefficient. Therefore, the transport of CRs from the disk to the halo is set by the magnetic field line random walk induced by large-scale turbulence. Second, we propose that the spectral steepening at $ TV $ is related to the typical maximum rigidity reached in the acceleration of CRs by the majority of supernova remnants, while we assume that only a fraction of sources, contributing to $ 10-20<!PCT!> $ of the CR population, can accelerate particles up to sim PV rigidities. Within this framework we show that it is possible to reproduce the proton and helium spectra from GV to multi-PV; the $p$/He ratio; the spectra of CRs from lithium to iron; the $ p $ flux and the $ p /p$ ratio; and the abundance ratios B/C, B/O, C/O, Be/C, Be/O, and Be/B. We also discuss the Be Be ratio in view of the recent AMS02 preliminary measurements.