A controlled transition between two different ion acceleration mechanisms would pave the way to achieving different ion energies and spectral features within the same experimental set up, depending on the region of operation. Based on numerical simulations conducted over a wide range of experimentally achievable parameter space, reported here is a comprehensive investigation of the different facets of ion acceleration by relativistically intense circularly polarized laser pulses interacting with thin near-critical-density plasma targets. The results show that the plasma thickness, exponential density gradient, and laser frequency chirp can be controlled to switch the interaction from the transparent operating regime to the opaque one, thereby enabling the choice of a Maxwellian-like ion energy distribution with a cutoff energy in the relativistically transparent regime or a quasi-monoenergetic spectrum in the opaque regime. Next, it is established that a multispecies target configuration can be used effectively for optimal generation of quasi-monoenergetic ion bunches of a desired species. Finally, the feasibility is demonstrated for generating monoenergetic proton beams with energy peak at E≈20–40 MeV and a narrow energy spread of ΔE/E≈18%–28.6% confined within a divergence angle of ∼175 mrad at a reasonable laser peak intensity of I0 ≃ 5.4 × 1020 W/cm2.