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We aim to investigate the influence of the eccentricity and inclinationdamping due to planet-disc interactions on the final configurations of thesystems, generalizing previous studies on the combined action of the gas discand planet-planet scattering during the disc phase. Instead of the simplistic$K$-prescription, our n-body simulations adopt the damping formulae foreccentricity and inclination provided by the hydrodynamical simulations of ourcompanion paper. We follow the evolution of $11000$ numerical experiments ofthree giant planets in the late stage of the gas disc, exploring differentinitial configurations, planetary mass ratios and disc masses. The dynamicalevolutions of the planetary systems are studied along the simulations, withemphasis on the resonance captures and inclination-growth mechanisms. Most ofthe systems are found with small inclinations ($\le10^{\circ}$) at thedispersal of the disc. Even though many systems enter an inclination-typeresonance during the migration, the disc usually damps the inclinations on ashort timescale. Although the majority of the multiple systems in our resultsare quasi-coplanar, $\sim5\%$ of them end up with high mutual inclinations($\ge10^{\circ}$). Half of these highly mutually inclined systems result fromtwo- or three-body MMR captures, the other half being produced by orbitalinstability and/or planet-planet scattering. When considering the long-termevolution over $100$ Myr, destabilization of the resonant systems is common,and the percentage of highly mutually inclined systems still evolving inresonance drops to $30\%$. Finally, the parameters of the final systemconfigurations are in very good agreement with the semi-major axis andeccentricity distributions in the observations, showing that planet-planetinteractions during the disc phase could have played an important role insculpting planetary systems.

Highly inclined and eccentric massive planets. II. Planet-planet interactions during the disc phase