Tidal disruption events (TDEs) provide a unique laboratory for studying transient accretion, outflows, particle acceleration, and the possible connection between stellar disruptions and high-energy neutrinos. Motivated by recent candidate TDE--neutrino associations and by the forthcoming sensitivity of multimessenger facilities, we investigated under which physical conditions TDEs can be detected in MeV, GeV, and TeV gamma rays and in high-energy neutrinos. We developed a lepto-hadronic emission framework and applied it to three representative sources: AT2019dsg, AT2019ehz, and ASASSN-14li. For each source we explored a set of physically motivated models that vary the proton and electron spectral indices, the minimum Lorentz factor of non-thermal protons, the particle energy partition, the acceleration efficiency, the magnetic compactness, and the presence of a compact corona. We computed the broadband spectral energy distributions and the associated muon-neutrino spectra, and compared them with reference sensitivities for COSI, /LAT, CTAO, and KM3NeT/ARCA. We find that hard proton spectra and/or large minimum proton Lorentz factors are the most favourable conditions for TeV gamma-ray and neutrino detectability, while GeV-bright models can be predominantly leptonic and neutrino-quiet. AT2019dsg and AT2019ehz can reach the CTAO and KM3NeT benchmarks in hadronically favourable configurations, whereas ASASSN-14li is more naturally bright in the MeV--GeV band and constrained by its radio synchrotron emission. Our results highlight the importance of combining MeV, GeV, TeV, radio, and neutrino observations to distinguish between transparent, hidden, and lepton-dominated TDE emission regimes. Fermi
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