Homogeneous team formation is the task of grouping individuals into teams, each of which consists of members who fulfill the same set of prespecified properties. In this theoretical work, we propose, motivate, and analyze a combinatorial model where, given a matrix over a finite alphabet whose rows correspond to individuals and columns correspond to attributes of individuals, the user specifies lower and upper bounds on team sizes as well as combinations of attributes that have to be homogeneous (that is, identical) for all members of the corresponding teams. Furthermore, the user can define a cost for assigning any individual to a certain team. We show that some special cases of our new model lead to NP-hard problems while others allow for (fixed-parameter) tractability results. For example, the problem is already That version concentrates on the anonymization aspects of the model. In our new version we slightly extend our model and show how it applies to (homogeneous) clustering of individuals, that is, to homogeneous team formation. Indeed, we now claim that the models and ideas better fit with these applications than with the previous data anonymization motivation. Apart from full proofs omitted in the extended abstract and also adapting our old ideas to the new extended model, the current article also contains a new and easier proof of NP-hardness, a new proof for showing that polynomial-time data reduction in term of so-called polynomial-size problem kernels is unlikely to exist with respect to certain parameterizations, and a new algorithm for the (still NP-hard) special case ignoring costs. Many of the new findings are part of the diploma thesis [18] NP-hard even if (i) there are no lower and upper bounds on the team sizes, (ii) all costs are zero, and (iii) the matrix has only two columns. In contrast, the problem becomes fixed-parameter tractable for the combined parameter "number of possible teams" and "number of different individuals", the latter being upper-bounded by the number of rows.