The paper continues our investigations of three-dimensional nonlinear resonant fluid sloshing in a square-base basin with finite depth (mean depth/tank length ratio $h\,{\ge}\, 0.3$). The sloshing is forced by a combined sway/surge resonant harmonic excitation of the two lowest natural modes. The new studies are strongly motivated by a discrepancy between previous quantitative theoretical results and experimental measurements and consist of a more precise description of the strong nonlinear amplification of higher modes. The latter is justified here by secondary resonance. Effective frequency domains of the secondary resonance are quantified. An adaptive asymptotic modal theory improves agreement with earlier and new experimental data both in the transient and steady-state conditions. Local breaking and overturning near the walls, that may lead to a ‘switch’ between distinct steady regimes, increase both global damping and generate random-like excitation of higher modes, are extensively discussed.