Abstract Swift J1727.8–1613 is a black hole X-ray binary newly discovered in 2023. We perform spectral analysis with simultaneous Insight-HXMT, NICER, and NuSTAR observations when the source was approaching the hard intermediate state. Such a joint view reveals an additional hard component apart from the normally observed hard component with reflection in the spectrum, to be distinguished from the usual black hole X-ray binary systems. By including this extra component in the spectrum, we have measured a high spin of 0.98 − 0.07 + 0.02 and an inclination of around 40 − 0.8 + 1.2 °, which is consistent with NICER results reported before. However, we find that the additional spectral component cannot be exclusively determined due to the model degeneracy. Accordingly, a possible jet/corona configuration is adjusted to account for the spectral fitting with different model trials. The extra component may originate either from a relativistic jet or a jet base/corona underneath a slow jet.