  In addition to the Standard Model, the introduction of a singlet complex
scalar field that acquires vacuum expectation value may give rise to a
cosmologically stable pseudo-Nambu-Goldstone boson (pNGB), a suitable dark
matter (DM) candidate. This work extends this scenario by including a second
cosmologically stable particle: a fermion singlet. The pNGB and the new fermion
can be regarded as DM candidates simultaneously, both interacting with the
Standard Model through Higgs portals via two non-degenerate Higgs bosons. We
explore the thermal freeze-out of this scenario, with particular emphasis on
the increasing yield of the pNGB before it completely decouples (recently
called Bouncing DM). We test the model under collider bounds, relic abundance,
and direct detection, and we explore some indirect detection observables today.
