We present an exact solution of the linearised semiclassical Boltzmann equation (SBE) beyond the relaxation-time approximation for multifold semimetals under arbitrarily oriented electric and magnetic fields. The framework treats the Berry curvature, orbital magnetic moment, Lorentz-force operator, and scattering terms on equal footing. Momentum-independent scattering-amplitudes couple the Fermi-surface sheets through intranode, interband, and internode processes. The scattering kernel has a finite rank and the SBE reduces to a linear system for a few moments, which is closed by the electron-number constraint. We apply this approach to four systems involving quadratic-corrected triple-point, Weyl, and Rarita-Schwinger-Weyl nodes, including tilted triple-point nodes. We obtain analytical results at zero field and to leading orders in the magnetic field, alongside numerical solutions for the full field dependence. Our results elucidate the roles of the topological properties, Lorentz-force operator, tilt, and intra- and internode scatterings in shaping the magnetoconductivity and planar-Hall response for noncollinear fields. It cures severe shortcomings of previous treatments like incomplete ansätze and incomplete treatment of the Lorentz-force operator.