While three-dimensional (3D) printing has been making significant strides over the past decades, it still trails behind mainstream manufacturing due to its lack of scalability in both print size and print speed. Cooperative 3D printing (C3DP) is an emerging technology that holds the promise to mitigate both of these issues by having a swarm of printhead-carrying mobile robots working together to finish a single print job cooperatively. In our previous work, we have developed a chunk-based printing strategy to enable the cooperative 3D printing with two fused deposition modeling (FDM) mobile 3D printers, which allows each of them to print one chunk at a time without interfering with the other and the printed part. In this paper, we present a novel method in discretizing the continuous 3D printing process, where the desired part is discretized into chunks, resulting in multi-stage 3D printing process. In addition, the key contribution of this study is the first working scaling strategy for cooperative 3D printing based on simple heuristics, called scalable parallel arrays of robots for 3DP (SPAR3), which enables many mobile 3D printers to work together to reduce the total printing time for large prints. In order to evaluate the performance of the printing strategy, a framework is developed based on directed dependency tree (DDT), which provides a mathematical and graphical description of dependency relationships and sequence of printing tasks. The graph-based framework can be used to estimate the total print time for a given print strategy. Along with the time evaluation metric, the developed framework provides us with a mathematical representation of geometric constraints that are temporospatially dynamic and need to be satisfied in order to achieve collision-free printing for any C3DP strategy. The DDT-based evaluation framework is then used to evaluate the proposed SPAR3 strategy. The results validate the SPAR3 as a collision-free strategy that can significantly shorten the printing time (about 11 times faster with 16 robots for the demonstrated examples) in comparison with the traditional 3D printing with single printhead.