Additive manufacturing (AM) has evolved from prototyping to functional part fabrication for a wide range of applications. Challenges exist in developing new product design methodologies to utilize AM-enabled design freedoms while limiting costs at the same time. When major design changes are made to a part, undesired high cost increments may be incurred due to significant adjustments of AM process settings. In this research, we introduce the concept of an additive manufactured variable product platform and its associated process setting platform. Design and process setting adjustments based on a reference part are constrained within a bounded feasible space (FS) in order to limit cost increments. In this paper, we develop a cost-driven design methodology for product families implemented with additive manufactured variable platforms. A fuzzy time-driven activity-based costing (FTDABC) approach is introduced to estimate AM production costs based on process settings. Time equations in the FTDABC are computed in a trained adaptive neuro-fuzzy inference system (ANFIS). The process setting adjustment's FS boundary is identified by solving a multi-objective optimization problem. Variable platform design parameter limitations are computed in a Mamdani-type expert system, and then used as constraints in the design optimization to maximize customer perceived utility. Case studies on designing an R/C racing car family illustrate the proposed methodology and demonstrate that the optimized additive manufactured variable platforms can improve product performances at lower costs than conventional consistent platform-based design.