  The presence of stable topological defects in a two-dimensional (\textit{d} =
2) liquid crystal model allowing molecular reorientations in three dimensions
(\textit{n} = 3) was largely believed to induce defect-mediated
Berzenskii-Kosterlitz-Thouless (BKT) type transition to a low temperature phase
with quasi long-range order. However, earlier Monte Carlo (MC) simulations
could not establish certain essential signatures of the transition, suggesting
further investigations. We study this model by computing its equilibrium
properties through MC simulations, based on the determination of the density of
states of the system. Our results show that, on cooling, the high temperature
disordered phase deviates from its initial progression towards the topological
transition, crossing over to a new fixed point, condensing into a nematic phase
with exponential correlations of its director fluctuations. The thermally
induced topological kinetic processes continue, however limited to the length
scales set by the nematic director fluctuations, and lead to a second
topological transition at a lower temperature. We argue that in the (\textit{d}
= 2, \textit{n} = 3) system with a biquadratic Hamiltonian, the presence of
additional molecular degree of freedom and local $Z_{2}$ symmetry associated
with lattice sites, together promote the onset of an additional relevant
scaling field at matching length scales in the high temperature region, leading
to a crossover.
