Observations have confirmed the existence of multiple-planet systems containing a hot Jupiter and smaller planetary companions. Examples include WASP-47, Kepler-730, and TOI-1130. We examine the plausibility of forming such systems in situ using $N$-body simulations that include a realistic treatment of collisions, an evolving protoplanetary disc and eccentricity/inclination damping of planetary embryos. Initial conditions are constructed using two different models for the core of the giant planet: a seed-model and an equal-mass-model. The former has a more massive protoplanet placed among multiple small embryos in a compact configuration. The latter consists only of equal-mass embryos. Simulations of the seed-model lead to the formation of systems containing a hot Jupiter and super-Earths. The evolution consistently follows four distinct phases: early giant impacts; runaway gas accretion onto the seed protoplanet; disc damping-dominated evolution of the embryos orbiting exterior to the giant; a late chaotic phase after dispersal of the gas disc. Approximately 1% of the equal-mass simulations form a giant and follow the same four-phase evolution. Synthetic transit observations of the equal-mass simulations provide an occurrence rate of 0.26% for systems containing a hot Jupiter and an inner super-Earth, similar to the 0.2% occurrence rate from actual transit surveys, but simulated hot Jupiters are rarely detected as single transiting planets, in disagreement with observations. A subset of our simulations form two close-in giants, similar to the WASP-148 system. The scenario explored here provides a viable pathway for forming systems with unusual architectures, but does not apply to the majority of hot Jupiters.
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