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Bol operators (Bols for short) are differential operators invariant under theprojective action of $\mathfrak{pgl}(2)\simeq\mathfrak{sl}(2)$ between spacesof weighted densities on the 1-dimensional manifold.  Here, we described analogs of Bols: $\mathfrak{pgl}(a+1\vert b)$-invariantdifferential operators between spaces of tensor fields on $(a\vertb)$-dimensional supermanifolds with irreducible, as $\mathfrak{gl}(a\vertb)$-modules, fibers of arbitrary, even infinite, dimension for certain ``key"values of $a$ and $b$ -- the ones for which the solution is describable. Wediscovered 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 naturalsuperization of Bol's result, additional to the cases of super analogs of Bolsbetween spaces of weighted densities on the $1\vert n$-dimensional superstringswith a~contact structure we classified in arXiv:2110.10504.  In the case of fibers of dimension $>1$, there are $(a+b-1)$-parameterfamilies of Bols, whereas there are no non-scalar non-zero differentialoperators between spaces of weighted densities. These two extreme answersjustify the selection of cases here.

Analogs of Bol operators for $\mathfrak{pgl}(a+1\vert b)\subset \mathfrak{vect}(a\vert b)$