The individual loudness perception of a patient plays an important role in hearing aid satisfaction and use in daily life. Hearing aid fitting and development might benefit from individualized loudness models (ILMs), enabling better adaptation of the processing to individual needs. The central question is whether additional parameters are required for ILMs beyond non-linear cochlear gain loss and linear attenuation common to existing loudness models for the hearing impaired (HI). Here, loudness perception in eight normal hearing (NH) and eight HI listeners was measured in conditions ranging from monaural narrowband to binaural broadband, to systematically assess spectral and binaural loudness summation and their interdependence. A binaural summation stage was devised with empirical monaural loudness judgments serving as input. While NH showed binaural inhibition in line with the literature, binaural summation and its inter-subject variability were increased in HI, indicating the necessity for individualized binaural summation. Toward ILMs, a recent monaural loudness model was extended with the suggested binaural stage, and the number and type of additional parameters required to describe and to predict individual loudness were assessed. In addition to one parameter for the individual amount of binaural summation, a bandwidth-dependent monaural parameter was required to successfully account for individual spectral summation.