We present a multiphase, resolved study of the galactic wind extending from the nearby starburst galaxy NGC 4666. For this, we use VLT/MUSE observations from the GECKOS program and H i data from the WALLABY survey. We identify both ionized and H i gas in a biconical structure extending to at least z~ 8 kpc from the galaxy disc, with increasing velocity offsets above the mid-plane in both phases, consistent with a multiphase wind. The measured electron density, using [S ii], differs significantly from standard expectations of galactic winds. We find electron density declines from the galaxy centre to ~ 2 kpc, then rises again, remaining high (~ 100-300 cm⁻³) out to ~5 kpc. We find that H i dominates the mass loading. The total H i mass outflow rate (above $z~>2$ kpc) is between 5-13~ M~ yr⁻¹, accounting for uncertainties from disc-blurring and group interactions. The total ionized mass outflow rate (traced by Hα) is between 0.5 and 5~ M~ yr⁻¹, depending on nₑ(z) assumptions. From ALMA/ACA observations, we place an upper limit on CO flux in the outflow which correlates to 2.9~ M~ yr⁻¹. We also show that the entire outflow is not limited to the bicone, but a secondary starburst at the edge generates a more widespread outflow, which should be included in simulations. The cool gas in NGC 4666 wind has insufficient velocity to escape the halo of a galaxy of its mass, especially because most of the mass is present in the slower atomic phase. This strong biconical wind contributes to gas cycling around the galaxy.
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