  Giant resonances (GRs) are a striking manifestation of collective motions in
atomic nuclei. The present paper is the second in a series of four dedicated to
the use of the projected generator coordinate method (PGCM) for the ab initio
determination of the isoscalar giant monopole resonance (GMR) in closed- and
open-shell mid-mass nuclei.
  While the first paper was dedicated to quantifying various uncertainty
sources, the present paper focuses on the first applications to three
doubly-open shell nuclei, namely $^{46}$Ti, $^{28}$Si and $^{24}$Mg. In
particular, the goal is to investigate from an ab initio standpoint (i) the
coupling of the GMR with the giant quadrupole resonance (GQR) in
intrinsically-deformed nuclei, (ii) the possible impact of shape coexistence
and shape mixing on the GMR, (iii) the GMR based on shape isomers and (iv) the
impact of anharmonic effects on the monopole response. The latter is studied by
comparing PGCM results to those obtained via the quasi-particle random phase
approximation (QRPA), the traditional many-body approach to giant resonances,
performed in a consistent setting.
  Eventually, PGCM results for sd-shell nuclei are in excellent agreement with
experimental data, which is attributed to the capacity of the PGCM to capture
the important fragmentation of the monopole response in light,
intrinsically-deformed systems. Still, the comparison to data in $^{28}$Si and
$^{24}$Mg illustrates the challenge (and the potential benefit) of extracting
unambiguous experimental information.
