ABSTRACT 1RXS J180408.9–342058 is a low-mass X-ray binary hosting a neutron star, which shows X-ray activity at very different mass-accretion regimes, from very faint to almost the Eddington luminosity. In this work, we present a comprehensive X-ray study of this source using data from the Neil Gehrels Swift Observatory, NuSTAR, and INTEGRAL/JEM-X. In order to follow the spectral evolution, we analysed the 2015 outburst using Swift data and three NuSTAR observations. Besides the canonical hard and soft spectral states, we identified the rarely observed intermediate state. This was witnessed by the appearance of the accretion disc emission in the spectrum (at kTdisc ∼0.7 keV) and the simultaneous cooling of the hot corona. In addition, we also unveiled a hard tail above 30 keV in this state. In the hard state, a thermal Comptonization model with two seed photons populations (kTs,1 ∼ 1.5 keV and kTs,2 ∼ 0.4 keV, respectively) and a hot Comptonizing plasma, represents the physically best motivated scenario to describe the data. We also estimated a reflection fraction below 20 per cent in all states, while no constraints on the inclination and only lower limits on the inner disc radius could be inferred. Finally, we studied a number of type-I X-ray bursts displayed from the source, one of them at the Eddington limit (observed with JEM-X). Their characteristics, combined with the clocked behaviour observed during the intermediate state, point out H/He composition for the accreted material, which makes unlikely the helium dwarf nature for the companion.