Detailed knowledge of the inner-shell atomic structure of lowly-ionised species is lacking for most elements along the 6th row of the Periodic Table, from hafnium to bismuth. This paper presents 4f-photoabsorption spectra of Pt+ to Pt4+ ions, recorded between 69 and 127 eV (9.8 nm and 18 nm) using the dual laser plasma (DLP) method. Analysis of the spectra was supported by atomic structure calculations using the Cowan suite of codes, by relativistic time-dependent local-density approximation (RTDLDA) calculations, and by comparison along isoelectronic series, particularly with spectra of lowly-ionised gold plasmas. The RTDLDA calculations account for the influence of photoionisation and photoexcitaiton on the recorded spectra. The spectra show 4f → 5d, 6d, and 7d transitions, broadened by autoionisation.