  We generalize the construction of geometric superpolynomials for unibranch
plane curve singularities from our prior paper from rank one to any ranks. The
new feature is the definition of counterparts of Jacobian factors (directly
related to compactified Jacobians) for higher ranks, which is parallel to the
classical passage from invertible bundles to vector bundles over algebraic
curves. This is an entirely local theory, connected with affine Springer fibers
for non-reduced (germs of) spectral curves. We conjecture and justify
numerically the connection of our geometric polynomials in arbitrary ranks with
the corresponding DAHA superpolynomials of algebraic knots colored by columns.
