We present high precision negative ion thermal ionisation mass spectrometry (N‐TIMS) Os isotope measurement results for the DROsS reference material, to investigate the limits on the precision of TIMS‐based 186Os/188Os measurements. We use analytical conditions previously highlighted to optimise precision, present a new flexible data processing protocol, and measure 184Os on a Faraday Cup equipped with a 1012 Ω amplifier. Despite analytical protocols that minimise uncertainty from counting statistics and Johnson‐Nyquist noise, the intermediate measurement precision of our approach does not significantly improve on previous high precision Os isotope measurements, with the exception of 184Os/188Os. This is probably due to uncertainties in measured amplifier gain factors, which are greater when using mixed arrays of 1011 and 1012 Ω amplifiers than when using 1011 Ω amplifiers alone, though Faraday Cup deterioration could also contribute. We propose that multi‐dynamic Os isotope measurements could largely eliminate both of these uncertainties. Our 184Os/188Os measurement results are the most precise yet, yielding 184Os/188Os = 0.0013036 ± 0.0000007 (2s, n = 38). Additionally, we average our data with published data to recommend the following composition for DROsS: 186Os/188Os = 0.1199319 ± 0.0000024, 187Os/188Os = 0.1609227 ± 0.0000022, 189Os/188Os = 1.219709 ± 0.000010, 190Os/188Os = 1.983793 ± 0.000011.