We show that three dimensional "sliding" analogs of the Kosterlitz-Thouless phase, in stacked classical two-dimensional XY models and quantum systems of coupled Luttinger Liquids, can be enlarged by the application of a parallel magnetic field, which has the effect of increasing the scaling dimensions of the most relevant operators that can perturb the critical sliding phases. Within our renormalization group analysis, we also find that for the case of coupled Luttinger liquids, this effect is

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... nterleaved with the onset of the integer quantum Hall effect for weak interactions and fields. We comment on experimental implications for a conjectured smectic metal phase in the cuprates.