Solid surfaces located in the vicinity of a supersonic jet may affect its flow dynamics and greatly change the aeroacoustic characteristics. Large-eddy simulations (LES) are performed to investigate the plate effects on a highly-heated rectangular supersonic jet. The rectangular nozzle has an aspect ratio of 2.0 and is operated at the over-expanded condition with a nozzle pressure ratio of 3.0 and a nozzle temperature ratio of 7.0. Four cases, JetL0 to JetL3 with a plate-to-nozzle distance ranging from 0 to 3 times of the jet equivalent nozzle diameter are investigated. The large-scale implicit LES computations are performed by a well-validated in-house finite-volume based CFD code, which uses an artificial dissipation mechanism to represent the effect of small-scale turbulence and to damp the numerical oscillation near shocks. The temperature-dependent thermal properties of air in the highly-heated jets are considered by the chemical equilibrium assumption. Numerical results show that among the four cases, JetL0 with the plate directly attached at the nozzle lip shows significant different flow and acoustic fields from the others. It exhibits a longer jet potential core length but without forming a series of well-structured shock diamonds. The other cases show similar shock/expansion wave structures as observed in the free jet but their jet plumes bend towards the plate. This bending of jet leads to JetL1 scrubs over the plate in the downstream. The scrubbing effect, together with the unaffected shock-shear layer interactions and high plate pressure loading, makes JetL1 have a stronger OASPL in the near acoustic fields than the other cases. The spectrum analysis in the nozzle upstream direction shows that the plate removes or mitigates the screech tone observed in the free jet and slightly amplifies the acoustic amplitudes in the low-frequency range.