  We apply the generalized formalism and the techniques of the supersymmetric
(susy) quantum mechanics to the cases where the superpotential is
generated/defined by higher excited eigenstates (Robnik 1997, paper I). The
generalization is technically almost straightforward but physically quite
nontrivial since it yields an infinity of new classes of susy-partner
potentials, whose spectra are exactly identical except for the lowest $n+1$
states, if the superpotential is defined in terms of the $(n+1)$-st
eigenfunction, with $n=0$ reserved for the ground state. First we show that
there are practically no possibilities for shape invariant potentials based on
higher excited states. Then we calculate the isospectral partner potentials for
the following 1-dim potentials (after separation of variables where
appropriate): (i) 3-dim (spherically symmetric) harmonic oscillator, (ii) 3-dim
(isotropic) Kepler problem, (iii) Morse potential, (iv) P\"oschl-Teller type I
potential, and (v) the 1-dim box potential. In all cases except in (v) we get
new classes of solvable potentials. In (v) the partner potential to the box
potential is a special case of P\"oschl-Teller type I potential. potentials. In
this paper we present results of a straightforward further application of this
formalism to a few most important exactly solvable 1-dim potentials, namely (i)
spherically symmetric 3-dim harmonic oscillator, (ii) 3-dim isotropic
(spherically symmetric) Kepler potential, (iii) Morse potential, (iv)
P\"oschl-Teller type I potential, and (v) 1-dim box potential.
  PACS numbers: 03.65.-w, 03.65.Ge, 03.65.Sq
