In 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 good dark matter (DM) candidate with novel features at the phenomenological level, such as the reduction of the direct detection signal. This work extends this scenario by including a second cosmological stable particle: a fermion singlet. The pNGB and the new fermion can be regarded as DM candidates simultaneously, interacting with the Standard Model through a Higgs portal via two non-degenerate Higgs bosons. We explore the thermal freeze-out of this scenario, with special emphasis on the increasing yield of the pNGB before it completely freezes-out (recently called bouncing DM). We test the model under collider, relic abundance, and direct detection, and we explore the consequences of the yield bouncing on indirect detection observables today