  As is known, the Blaschke tensor $A$ (a symmetric covariant $2$-tensor) is
one of the fundamental M\"obius invariants in the M\"obius differential
geometry of submanifolds in the unit sphere $\mathbb S^n$, and the eigenvalues
of $A$ are referred to as the Blaschke eigenvalues. In this paper, we continue
our job for the study on the submanifolds in $\bbs^n$ with parallel Blaschke
tensors which we simply call {\em Blaschke parallel submanifolds} to find more
examples and seek a complete classification finally. The main theorem of this
paper is the classification of Blaschke parallel submanifolds in $\mathbb S^n$
with exactly three distinct Blaschke eigenvalues. Before proving this
classification we define, as usual, a new class of examples.
