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We report the discovery and analysis of a candidate triple-lens single-source (3L1S) microlensing event, OGLE-2019-BLG-1470. This event was first classified as a normal binary-lens single-source (2L1S) event, but a careful 2L1S modelling showed that it needs an additional lens or source to fit the observed data. It is found that the 3L1S model provides the best fit, but the binary-lens binary-source (2L2S) model is only disfavoured by $Δχ^2 \simeq 18$. All of the feasible models include a planet with planet-to-host mass-ratios $10^{-3} \lesssim q \lesssim 10^{-2}$. A Bayesian analysis based on a Galactic model indicates that the planet is super-Jovian, and the projected host-planet separation is about 3 $\mathrm{au}$. Specifically, for the best-fit 3L1S model, the two stars have masses of $M_1=0.57^{+0.43}_{-0.32}M_{\odot}$, and $M_2=0.18^{+0.15}_{-0.10}M_{\odot}$, with projected separation of $1.3^{+0.5}_{-0.5}$ $\mathrm{au}$, and the planetary mass is $M_3=2.2^{+1.8}_{-1.3}M_{\rm{Jupiter}}$. For the 2L2S model, the masses of the host star and the planet are $0.55^{+0.44}_{-0.31}M_{\odot}$ and $4.6^{+3.7}_{-2.6}M_{\rm{Jupiter}}$, respectively. By investigating the properties of all known microlensing planets in binary systems, we find that all planets in binary systems published by the KMTNet survey are located inside the resonant caustics range with $q \gtrsim 2 \times 10^{-3}$, indicating the incompleteness of the KMTNet sample for planets in binary systems. Thus, planets in binary systems cannot be included in the current study of the KMTNet mass-ratio function, and a systematic search for planetary anomalies in KMTNet microlensing light curves of binary systems is needed.