Many publicly-available data sources for the study of income distributions have been evidenced to suffer from measurement errors which are particularly important in the upper tail of the distribution. While various methods have been explored in the literature to correct for these measurement errors two issues have been largely left unattended. Firstly, a great majority of public-use data sources on incomes are only accesible in a grouped-data format, while in general the existing correction methods have only been developed to be applied using individual-level data. Secondly, while problems of very different nature may interact in the measurement errors of high incomes (notably those of under-reporting and undersampling of high incomes in income survey data), existing correction methods can only account for rather simplistic patterns of such measurement errors. This presentation proposes a general correction method integrating some of the pre-existing methods in the literature based on parametric Lorenz curves which allows for correcting simultaneously for under-reporting and for undersampling of high incomes when working with grouped data, while also allowing for other special cases of these two errors such as top-coding. The properties of the correction method along with grouped-data estimation strategies are explored in a Monte Carlo experiment framework, proposing separately a least-squares estimator for classical inference and an Approximate Bayesian Computation (ABC) estimator for Bayesian inference.