The 14N + 159Tb reaction was studied at 5 energies between 8 and 22 MeV/u via the measurement of particle-KX-ray coincidences with the charged particle detector placed near the grazing angle. With this method a very extensive set of partial cross sections d-sigma-d-omega(PLF, Zres) of projectile-like fragments (PLF's) as a function of the atomic number of the residual nucleus (Zres) was obtained and thus the cross-section balance determined. It is found that the inclusive cross sections can be accounted for to within ~20% by the sum of the (exclusive) partial cross sections with the use of average KX-ray multiplicities. From the partial cross sections it is deduced that a large fraction of the inclusive PLF cross sections originates from “non-binary” reaction channels, in which additional charged particles are emitted. The evaporation of light charged particles from the target-like fragment is observed to be only a minor source of these charge non-binary channels. At 115 and 168 MeV probabilities for sequential decay of primary fragments are obtained, which are in good agreement with results from particle-particle correlation measurements. The Qgg dependence does not give a satisfactory description of the cross sections for charge binary channels at the higher energies. The bulk of the reaction channels in which a PLF with Z ⩾ 3 is emitted can be attributed to a quasi-elastic peripheral collision, in which a primary fragment is formed in a particle stable or unstable state. The quasi-elastic character of these channels is underlined by γ-ray multiplicities measured in the same experiments.