  In this paper we continue our study of the Frobenius instability locus in the
coarse moduli space of semi-stable vector bundles of rank $r$ and degree $0$
over a smooth projective curve defined over an algebraically closed field of
characteristic $p>0$. In a previous paper we identified the "maximal" Frobenius
instability strata with opers (more precisely as opers of type $1$ in the
terminology of the present paper) and related them to certain Quot-schemes of
Frobenius direct images of line bundles. The main aim of this paper is to
describe for any integer $q \geq 1$ a conjectural generalization of this
correspondence between opers of type $q$ (which we introduce here) and
Quot-schemes of Frobenius direct images of vector bundles of rank $q$. We also
give a conjectural formula for the dimension of the Frobenius instability
locus.
