  Typical of modern quantum technologies employing nanomechanical oscillators
is to demand few mechanical quantum excitations, for instance, to prolong
coherence times of a particular task or, to engineer a specific non-classical
state. For this reason, we devoted the present work to exhibit how to bring an
initial thermalized nanomechanical oscillator near to its ground state.
Particularly, we focus on extending the novel results of D. D. B. Rao
\textit{et al.}, Phys. Rev. Lett. \textbf{117}, 077203 (2016), where a
mechanical object can be heated up, squeezed, or cooled down near to its ground
state through conditioned single-spin measurements. In our work, we study a
similar iterative spin-mechanical system when $N$ spins interact with the
mechanical oscillator. Here, we have also found that the postselection
procedure acts as a discarding process, i.e., we steer the mechanics to the
ground state by dynamically filtering its vibrational modes. We show that when
considering symmetric collective spin postselection, the inclusion of $N$ spins
into the quantum dynamics results highly beneficial. In particular, decreasing
the total number of iterations to achieve the ground-state, with a success rate
of probability comparable with the one obtained from the single-spin case.
