Business processes may accept variants based on specific business requirements of an organization, leading to the definition of a process family. There are many proposals for the modeling of the common and variable parts of a process family, as well as to support the customization of each process variant (i.e., process configuration or tailoring). In this article, we present the results of a detailed study about the modeling and customization of process families based on the Business Process Model and Notation (BPMN 2.0) standard, and we introduce BPMNext, a novel approach devised for this purpose. The language is an adaptation of BPMN 2.0 based on the ideas provided by vSPEM, a language for the modeling of software processes families. We also present a supporting tool and its application to a real case study about the assignment of positions in exchange programs.