We show that a one-dimensional quantum wire with as few as 2 channels of interacting fermions can host metallic states of matter that are stable against all perturbations up to $q^text{th}$-order in fermion creation/annihilation operators for any fixed finite $q$. The leading relevant perturbations are thus complicated operators that are expected to modify the physics only at very low energies, below accessible temperatures. The stability of these non-Fermi liquid fixed points is due to strong interactions between the channels, which can (but need not) be chosen to be purely repulsive. Our results might enable elementary physical realizations of these phases.
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