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Ultraluminous X-ray sources (ULXs) are a class of accreting compact objects with X-ray luminosities above 1e39 erg/s. The ULX population counts several hundreds objects but only a minor fraction is well studied. Here we present a detailed analysis of all ULXs hosted in the galaxy NGC 7456. It was observed in X-rays only once in the past (in 2005) by XMM-Newton, but the observation was short and strongly affected by high background. In 2018, we obtained a new, deeper (~90 ks) XMM-Newton observation that allowed us to perform a detailed characterization of the ULXs hosted in the galaxy. ULX-1 and ULX-2, the two brightest objects (Lx~(6-10)e39 erg/s), have spectra that can be described by a two-thermal component model as often found in ULXs. ULX-1 shows also one order of magnitude in flux variability on short-term timescales (hundreds to thousand ks). The other sources (ULX-3 and ULX-4) show flux changes of at least an order of magnitude, and these objects may be candidate transient ULXs although longer X-ray monitoring or further studies are required to ascribe them to the ULX population. In addition, we found a previously undetected source that might be a new candidate ULX (labelled as ULX-5) with a luminosity of ~1e39 erg/s and hard power-law spectral shape, whose nature is still unclear and for which a background Active Galactic Nucleus cannot be excluded. We discuss the properties of all the ULXs in NGC 7456 within the framework of super-Eddington accretion onto stellar mass compact objects. Although no pulsations were detected, we cannot exclude that the sources host neutron stars.