We present rest-frame optical spectra from the FMOS-COSMOS survey of twelve $z sim 1.6$ textit{Herschel} starburst galaxies, with Star Formation Rate (SFR) elevated by $times$8, on average, above the star-forming Main Sequence (MS). Comparing the H$alpha$ to IR luminosity ratio and the Balmer Decrement we find that the optically-thin regions of the sources contain on average only $sim 10$ percent of the total SFR whereas $sim90$ percent comes from an extremely obscured component which is revealed only by far-IR observations and is optically-thick even in H$alpha$. We measure the [NII]$_{6583}$/H$alpha$ ratio, suggesting that the less obscured regions have a metal content similar to that of the MS population at the same stellar masses and redshifts. However, our objects appear to be metal-rich outliers from the metallicity-SFR anticorrelation observed at fixed stellar mass for the MS population. The [SII]$_{6732}$/[SII]$_{6717}$ ratio from the average spectrum indicates an electron density $n_{rm e} sim 1,100 mathrm{cm}^{-3}$, larger than what estimated for MS galaxies but only at the 1.5$sigma$ level. Our results provide supporting evidence that high-$z$ MS outliers are the analogous of local ULIRGs, and are consistent with a major merger origin for the starburst event.
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