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Abstract We generalize the recently proposed continuum dark matter model to the case where the dark matter consists of a spin-1/2 or spin-1 gapped continuum. We construct simple continuum analogs of weakly interacting massive particles annihilating through the Z portal. We discuss all existing experimental constraints, with the strongest bounds arising from indirect detection and limits on continuum decays from the cosmic microwave background. Our models are phenomenologically viable for gap scales of 60–200 GeV (spin-1/2) and 35–90 GeV (spin-1), owing to the strong kinematic suppression of direct detection bounds which is unique to continuum states. We comment on future prospects for detection and suggest directions for further continuum model building.