ABSTRACT γ-ray-emitting narrow-line Seyfert 1 galaxies (γ-NLS1) constitute an intriguing small population of active galactic nuclei with γ-ray emission resembling low-power flat-spectrum radio quasars (FSRQ), but with differing physical properties. They are jetted, γ/radio-loud Seyfert galaxies, with relatively low black hole masses, accreting at exceptionally high, near-Eddington rates. Certain of these sources exhibit highly variable emission states on relatively short time-scales, the physical origin of which remains elusive. In this work, varying emission states of two bona fide NLS1s, 1H 0323+342 and PMN J0948+0022, and one little-studied FSRQ/intermediate object, B2 0954+25A, are examined. For each source, we analysed quasi-simultaneous multiwavelength data for different states of γ-ray activity and present the results of their broad-band emission modelling, taking into account all available physical constraints to limit the range of the model parameters. Two different scenarios are discussed, in the framework of a one-zone leptonic model, where the high-energy emission is due to the inverse Compton scattering of the disc and broad line region (BLR) or torus photons by relativistic electrons within the jet. The transition from low to high state is well described by variations of the jet parameters, leaving the external photon fields unchanged. The parameterization favours an emission scenario with particle injection on a stationary shock inside the jet. When considering all physical constraints, the disc and BLR scenario is preferred for all three sources. We use the multi-epoch modelling to characterize total jet powers and discuss the intrinsic nature of γ-NLS1 galaxies and FSRQs.