Can neutrinos change chirality by oscillating?

Active neutrinos are left-handed while sterile neutrinos are right-handed. There are speculations that active neutrinos can oscillate into sterile neutrinos. Can neutrinos change chirality by oscillating?

• The right handed partners of active neutrinos are also sterile, in this sense. Related question. – Cosmas Zachos Feb 10 at 1:25

If right handed neutrinos exist the neutrino dirac mass term $$-\mathcal{L}_D = m_D\overline{\nu}_L\nu_R +h.c.$$ couples left-handed to right-handed neutrinos and will therefore lead to left handed neutrinos "oscillating" into right handed ones and vice versa.
So yes there would be such oscillations. There are hints towards the existence of such oscillations induced by $$\sim1$$eV sterile neutrinos in the current oscillation data. The STERO experiment for example is searching for such oscillations. I already commented on this experiment and oscillation data within this post