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Aims.We investigate the photometric characteristics of a sample of intermediate-luminosity red transients (ILRTs), a class of elusive objects with peak luminosity between that of classical novae and standard supernovae. Our goal is to provide a stepping stone in the path to reveal the physical origin of such events, thanks to the analysis of the datasets collected. Methods.We present the multi-wavelength photometric follow-up of four ILRTs, namely NGC 300 2008OT-1, AT 2019abn, AT 2019ahd, and AT 2019udc. Through the analysis and modelling of their spectral energy distribution and bolometric light curves, we inferred the physical parameters associated with these transients. Results.All four objects display a single-peaked light curve which ends in a linear decline in magnitudes at late phases. A flux excess with respect to a single blackbody emission is detected in the infrared domain for three objects in our sample, a few months after maximum. This feature, commonly found in ILRTs, is interpreted as a sign of dust formation. Mid-infrared monitoring of NGC 300 2008OT-1 761 days after maximum allowed us to infer the presence of ∼10⁻³–10⁻⁵M_⊙of dust, depending on the chemical composition and the grain size adopted. The late-time decline of the bolometric light curves of the considered ILRTs is shallower than expected for⁵⁶Ni decay, hence requiring an additional powering mechanism. James Webb Space Telescope observations of AT 2019abn prove that the object has faded below its progenitor luminosity in the mid-infrared domain, five years after its peak. Together with the disappearance of NGC 300 2008OT-1 in Spitzer images seven years after its discovery, this supports the terminal explosion scenario for ILRTs. With a simple semi-analytical model we tried to reproduce the observed bolometric light curves in the context of a few solar masses ejected at few 10³km s⁻¹and enshrouded in an optically thick circumstellar medium.