  We propose a generalized version of knots-quivers correspondence, where the
quiver series variables specialize to arbitrary powers of the knot HOMFLY-PT
polynomial series variable. We explicitely compute quivers for large classes of
knots, as well as many homologically thick 9- and 10-crossings knots, including
the ones with the super-exponential growth property of colored HOMFLY-PT
polyomials. In addition, we propose a new, compact, quiver-like form for the
colored HOMFLY-PT polynomials, where the structure of colored differentials is
manifest. In particular, this form partially explains the non-uniqueness of
quivers corresponding to a given knot via knots-quivers correspondence.
