  Bol operators (Bols for short) are differential operators invariant under the
projective action of $\mathfrak{pgl}(2)\simeq\mathfrak{sl}(2)$ between spaces
of weighted densities on the 1-dimensional manifold.
  Here, we described analogs of Bols: $\mathfrak{pgl}(a+1\vert b)$-invariant
differential operators between spaces of tensor fields on $(a\vert
b)$-dimensional supermanifolds with irreducible, as $\mathfrak{gl}(a\vert
b)$-modules, fibers of arbitrary, even infinite, dimension for certain ``key"
values of $a$ and $b$ -- the ones for which the solution is describable. We
discovered many new operators for $(a|b)=(2|0), (0|3)$ and for the case of
$1\vert 1$-dimensional general superstring which looks like a~most natural
superization of Bol's result, additional to the cases of super analogs of Bols
between spaces of weighted densities on the $1\vert n$-dimensional superstrings
with a~contact structure we classified in arXiv:2110.10504.
  In the case of fibers of dimension $>1$, there are $(a+b-1)$-parameter
families of Bols, whereas there are no non-scalar non-zero differential
operators between spaces of weighted densities. These two extreme answers
justify the selection of cases here.
